Research

Refereed Publications

The refereed publications are divided into three sections of 

Stochastic analysis in PDE, Harmonic analysis in PDE, Mathematical Biology. 

They are all listed in counter-chronological order. (* indicates a graduate student at the time of submission and ** indicates an undergraduate student at the time of submission).

Stochastic analysis in PDE

1. Approximating three-dimensional magnetohydrodynamics system forced by space-time white noise.
     K. Yamazaki, J. Differential Equations, to appear. Its pre-print also available at arXiv:2002.12732 [math.AP].  

2. Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise.
     K. Yamazaki, Potential Anal. (2024), https://doi.org/10.1007/s11118-024-10128-6. Its pre-print also available at arXiv:2109.07015 [math.AP].

3. Non-uniqueness in law of the two-dimensional surface quasi-geostrophic equations forced by random noise.
     K. Yamazaki, Ann. Inst. Henri Poincare Probab. Stat., to appear. Its pre-print also available at arXiv:2208.05673 [math.PR].

4. Recent developments on convex integration technique applied to stochastic partial differential equations.
     K. Yamazaki, AWM Research Symposia, Association for Women in Mathematics Series, Springer, to appear.

5.  Non-uniqueness in law of three-dimensional Navier-Stokes equations diffused via a fractional Laplacian with power less than one half.
     K. Yamazaki, Stoch. PDE: Anal. Comp. (2023), https://doi.org/10.1007/s40072-023-00293-x. Its pre-print also available at arXiv:2104.10294 [math.PR].

6.  Three-dimensional magnetohydrodynamics system forced by space-time white noise.
     K. Yamazaki, Electron. J. Probab., 28 (2023), pp. 1-66. Its pre-print also availble at arXiv:1910.04820 [math.AP].

7. Non-uniqueness in law for the Boussinesq system forced by random noise.
     K. Yamazaki, Calc. Var. Partial Differential Equations, 61 (2022), https://doi.org/10.1007/s00526-022-02285-6. Its pre-print also available at arXiv:2101.05411 [math.AP]

8.  Non-uniqueness in law for two-dimensional Navier-Stokes equations with diffusion weaker than a full Laplacian.
     K. Yamazaki, SIAM J. Math. Anal., 54 (2022), pp. 3997-4042. Its pre-print available at arXiv:2008.04760 [math.AP].

9.  Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent.
     K. Yamazaki, Stochcastic Process. Appl., 147 (2022), pp. 226-269. Its pre-print available at arXiv:2006.11861 [math.AP].

10.  Ergodicity of Galerkin approximations of surface quasi-geostrophic equations and Hall-magnetohydrodynamics system forced by degenerate noise.
      K. Yamazaki, NoDEA Nonlinear Differential Equations Appl., 29 (2022), https://doi.org/10.1007/s00030-022-00753-8.

11.  Strong Feller property of the magnetohydrodynamics system forced by space-time white noise. [pdf]
      K. Yamazaki, Nonlinearity, 34 (2021), https://doi.org/10.1088/1361-6544/abfae7.

12.  Boussinesq system with partial viscous diffusion or partial thermal diffusion forced by a random noise. [pdf]
      K. Yamazaki, Appl. Math. Optim., (2021), https://doi.org/10.1007/s00245-021-09756-w.

13.  A note on the applications of Wick products and Feynman diagrams in the study of singular partial differential equations. [pdf]
      K. Yamazaki, J. Comput. Appl. Math., 388 (2021), 113338.

14.  Irreducibility of the three, and two and a half dimensional Hall-magnetohydrodynamics system. [pdf]
      K. Yamazaki, Phys. D, 401 (2020), 13299 https://doi.org/10.1016/j.physd.2019.132199.

15.  Stochastic Lagrangian formulations for damped Navier-Stokes equations and Boussinesq system and their applications. [pdf]
      K. Yamazaki, Commun. Stoch. Anal., 12 (2018), pp. 447-471.

16.  Gibbsian dynamics and ergodicity of magnetohydrodynamics and related systems forced by random noise. [pdf]
      K. Yamazaki, Stoch. Anal. Appl., 37 (2019), pp. 412-444.

The Version of Record of this manuscript has been published and is available in Stochastic Analysis and Applications, February 26, 2019, 10.1080/07362994.2019.1575237.

17. Markov selections for the magnetohydrodynamics and the Hall-magnetohydrodynamics systems. [pdf]
      K. Yamazaki, J. Nonlinear Sci., 29 (2019), pp. 1761-1812. DOI: 10.1007/s00332-019-09530-x. This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science.

18.  Well-posedness of Hall-magnetohydrodynamics system forced by Levy noise. [pdf]
      K. Yamazaki and M. T. Mohan, Stoch. PDE: Anal. Comp., 7 (2019), pp. 331--378, https://doi.org/10.1007/s40072-018-0129-6. This is a post-peer-review, pre-copyedit version of an article to appear in Stochastics and Partial Differential Equations: Analysis and Computations.

19.  Two examples on the property of the noise in the systems of equations of fluid mechanics. [pdf]
      K. Yamazaki, J. Comput. Appl. Math., 362 (2019), pp. 460-470. https://doi.org/10.1016/j.cam.2018.09.025.

20.  Ergodicity of a Galerkin approximation of three-dimensional magnetohydrodynamics system forced by a degenerate noise. [pdf]
      K. Yamazaki, Stochastics, 91 (2019), pp. 114-142. A pre-print version is available on arxiv at https://arxiv.org/abs/1809.00721.

21.  Large deviation principle for the micropolar, magneto-micropolar fluid systems. [pdf]
      K. Yamazaki, Discrete Contin. Dyn. Syst. Ser. B, 23 (2018), pp. 913-938.

The final publication is available at http://aimsciences.org/article/doi/10.3934/dcdsb.2018048.

22. Smoothness of Malliavin derivatives and dissipativity of solution to two-dimensional micropolar fluid system. [pdf]
      K. Yamazaki, Random Oper. Stoch. Equ., 25 (2017), pp. 131-153.

23.  Gibbsian dynamics and ergodicity of stochastic micropolar fluid system. [pdf]
      K. Yamazaki, Appl. Math. Optim., 79 (2019), pp. 1-40, doi:10.1007/s00245-017-9419-z. The final publication is available at Springer via http://dx.doi.org/10.1007/s00245-017-9419-z.

24.  Exponential convergence of the stochastic micropolar and magneto-micropolar fluid systems. [pdf]
      K. Yamazaki, Commun. Stoch. Anal., 10 (2016), pp. 271-295.

25.  Stochastic Hall-magneto-hydrodynamics system in three and two and a half dimensions. [pdf]
      K. Yamazaki, J. Stat. Phys., 166 (2017), pp. 368-397. The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-016-1683-9.

26.  Ergodicity of the two-dimensional magnetic Benard problem. [pdf]
      K. Yamazaki, Electron. J. Differential Equations, 2016 (2016), pp. 1-24. 

27.  Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system.
      K. Yamazaki, Adv. Differential Equations, 21 (2016), pp. 1085-1116.

28.  Global martingale solution for the stochastic Boussinesq system with zero dissipation. [pdf]

K. Yamazaki, Stoch. Anal. Appl., 34 (2016), pp. 404-426.

29.  Recent developments on the micropolar and magneto-micropolar fluid systems: deterministic and stochastic perspectives, in Stochastic Equations for Complex Systems: Theoretical and Computational Topics (eds. S. Heinz and H. Bessaih).
      K. Yamazaki, Springer International Publishing (2015), pp. 85–103. [pdf]

30.  3-D stochastic micropolar and magneto-micropolar fluid systems with non-Lipschitz multiplicative noise. [pdf]
      K. Yamazaki, Commun. Stoch. Anal., 8 (2014), pp. 413-437.

Harmonic analysis in PDE

1. Remarks on the global regularity issue of the two and a half dimensional Hall-magnetohydrodynamics system.
     M. M. Rahman* and K. Yamazaki, Z. Angew. Math. Phys., 73 (2022), pp. 1--29. Its pre-print also available at arXiv:2206.12026 [math.AP], 2022.

2.  Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three.
     A. Larios, M. M. Rahman*, and K. Yamazaki, J. Nonlinear Sci., 32 (2022), https://doi.org/10.1007/s00332-022-09828-3. Also available at arXiv:2112.07634 [math.AP]

3.  On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation. [pdf]
     A. Larios and K. Yamazaki, Phys. D, 411 (2020), 132560. 

4.  Remarks on the three and two and a half dimensional Hall-magnetohydrodynamics system: deterministic and stochastic cases. [pdf]
     K. Yamazaki, Complex Analysis and its Synergies, 5 (2019), https://doi.org/10.1007/s40627-019-0033-5.

5.  Second proof of the global regularity of the two-dimensional MHD system with full diffusion and arbitrary weak dissipation. [pdf]
     K. Yamazaki, Methods Appl. Anal., International Press of Boston, 25 (2018), pp. 73-96.

6.  On the global regularity issue of the two-dimensional magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian. [pdf]
     K. Yamazaki, Nonlinear dispersive waves and fluids, pp. 251-264, Contemp. Math., 725, Amer. Math. Soc., Providence, RI, 2019.

7.  Global regularity of logarithmically supercritical MHD system with improved logarithmic powers. [pdf]
     K. Yamazaki, Dyn. Partial Differ. Equ., 15 (2018), pp. 147-173.

8.  Horizontal Biot-Savart law in general dimension and an application to the 4D magneto-hydrodynamics.
     K. Yamazaki, Differential Integral Equations, 31, 3/4 (2018), pp. 301-328.

9.  On the Navier-Stokes equations in scaling-invariant spaces in any dimension. [pdf]
     K. Yamazaki, Rev. Mat. Iberoam., 34 (2018), pp. 1515-1540. DOI: 10.4171/rmi/1034.

10.  Global regularity of generalized magnetic Benard problem.  [pdf]
      K. Yamazaki, Math. Methods Appl. Sci., 40 (2017), pp. 2013-2033, doi: 10.1002/mma.4116.

11.  Regularity results on the Leray-alpha magnetohydrodynamics systems. [pdf]
      D. KC* and K. Yamazaki, Nonlinear Anal. Real World Appl., 32 (2016), pp. 178-197.

12.  Regularity criteria of the 4D Navier-Stokes equations involving two velocity field components. [pdf]
      K. Yamazaki, Commun. Math. Sci., 14 (2016), pp. 2229-2252.

13.  Recent developments on the component reduction results of Serrin-type regularity criterion for equations concerning fluid. [pdf]
      K. Yamazaki, Turbulence, Waves and Mixing in Honour of Lord Julian Hunt’s 75th Birthday edited by S. G. Sajjadi and H. J. S. Fernando, July 2016, King’s College, Cambridge, U.K., 68-70.

14.  A remark on the two-dimensional magnetohydrodynamics-alpha system. [pdf]
      K. Yamazaki, J. Math. Fluid Mech., 18 (2016), pp. 609-623.

15.  Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component. [pdf]
      K. Yamazaki, Nonlinear Anal., 135 (2016), pp. 73-83.

16.  Global regularity of logarithmically supercritical 3-D LAMHD-alpha system with zero diffusion. [pdf]
      K. Yamazaki, J. Math. Anal. Appl., 436 (2016), pp. 835-846.

17.  On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces. [pdf]
      K. Yamazaki, Bull. Sci. Math., 140 (2016), pp. 575-614.

18.  Global regularity of N-dimensional generalized MHD system with anisotropic dissipation and diffusion. [pdf]
      K. Yamazaki, Nonlinear Anal., 122 (2015), pp. 176-191.

19.  Logarithmically extended global regularity result of Lans-alpha MHD system in two-dimensional space. [pdf]
      D. KC* and K. Yamazaki, J. Math. Anal. Appl., 425 (2015), pp. 234-248.

20.  Global regularity of the two-dimensional magneto-micropolar fluid system with zero angular viscosity. [pdf]
      K. Yamazaki, Discrete Contin. Dyn. Syst., 35 (2015), pp. 2193-2207.

21.  (N-1) velocity components condition for the generalized MHD system in N-dimension. [pdf]
      K. Yamazaki, Kinet. Relat. Models, 7 (2014), pp. 779-792.

22.  Regularity criteria of porous media equation in terms of one partial derivative or pressure field. [pdf]
      K. Yamazaki, Commun. Math. Sci., 13 (2015), pp. 461-476.

23.  Component reduction for regularity criteria of the three-dimensional magnetohydrodynamics systems. [pdf]
      K. Yamazaki, Electron. J. Differential Equations, 2014, 98 (2014), pp. 1-18.

24.  Regularity criteria of MHD system involving one velocity and one current density component. [pdf]
      K. Yamazaki, J. Math. Fluid Mech., 16 (2014), pp. 551-570.

25.  Remarks on the Regularity criteria of three-dimensional MHD system in terms of two velocity field components. [pdf]
      K. Yamazaki, J. Math. Phys., 55, 031505 (2014).

26.  On the global regularity of two-dimensional generalized magnetohydrodynamics system. [pdf]
      K. Yamazaki, J. Math. Anal. Appl., 416 (2014), pp. 99-111.

27.  On the global regularity of N-dimensional generalized Boussinesq system. [pdf]
      K. Yamazaki, Appl. Math., 60 (2015), pp. 109-133.

28.  Global regularity of logarithmically supercritical MHD system with zero diffusivity. [pdf]
      K. Yamazaki, Appl. Math. Lett., 29 (2014), pp. 46-51.

29.  Regularity criteria of supercritical beta-generalized quasi-geostrophic equation in terms of partial derivatives. [pdf]
      K. Yamazaki, Electron. J. Differential Equations, 2013, 217 (2013), pp. 1-12.

30.  On the global well-posedness of N-dimensional generalized MHD system in anisotropic spaces.
      K. Yamazaki, Adv. Differential Equations, 19, 3-4 (2014), pp. 201-224.

31.  Remarks on the global regularity of two-dimensional magnetohydrodynamics system with zero dissipation. [pdf]
      K. Yamazaki, Nonlinear Anal., 94 (2014), pp. 194-205.

32.  Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems. [pdf]
      K. Yamazaki, J. Math. Phys., 54, 011502 (2013).

33.  On the regularity criteria of a surface quasi-geostrophic equation. [pdf]
      K. Yamazaki, Nonlinear Anal., 75 (2012), pp. 4950-4956.

34.  On the global regularity of generalized Leray-alpha type models. [pdf]
      K. Yamazaki, Nonlinear Anal., 75 (2012), pp. 503-515.

35.  Global well-posedness of transport equation with nonlocal velocity in Besov spaces with critical and supercritical dissipation. [pdf]
      K. Yamazaki, Nonlinearity, 24 (2011), pp. 2047-2062.

36.  Remarks on the method of modulus of continuity and the modified dissipative Porous Media Equation. [pdf]
      K. Yamazaki, J. Differential Equations, 250 (2011), pp. 1909-1923.

Mathematical Biology

1. Improved uniform persistence for partially diffusive models of infectious diseases: cases of avian influenza and Ebola virus disease.
     R. Covington**, S. Patton**, E. Walker**, and K. Yamazaki, Math. Biosci. Eng., 20 (2023), pp. 19686-19709. 

2. A partially diffusive cholera model based on a general second-order differential operator. [pdf]
     J. Wang, C. Yang*, and K. Yamazaki, J. Math. Anal. Appl., 501 (2021), 125181.

3.  Zika virus dynamics partial differential equations model with sexual transmission route. [pdf]
     K. Yamazaki, Nonlinear Anal. Real World Appl., 50 (2019), pp. 290–315, https://doi.org/10.1016/j.nonrwa.2019.05.003.

4.  Threshold dynamics of reaction-diffusion partial differential equations model of Ebola virus disease. [pdf]
     K. Yamazaki, Int. J. Biomath., 11 (2018), 1850108, https://doi.org/10.1142/S1793524518501085.

5.  Global well-posedness of infectious disease models without life-time immunity: the cases of cholera and avian influenza. [pdf]
     K. Yamazaki, Math. Med. Biol., 35 (2018), pp. 428-445. DOI: 10.1093/imammb/dqx016. The final publication is available at https://doi.org/10.1093/imammb/dqx016.

6.  Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model. [pdf]
     K. Yamazaki and X. Wang, Math. Biosci. Eng., 14 (2017), pp. 559-579.

7.  Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model. [pdf]
     K. Yamazaki and X. Wang, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), pp. 1297-1316.

Posted only on ArXiV

1. Non-uniqueness in law of the surface quasi-geostrophic equations: the case of linear multiplicative noise.
     K. Yamazaki, arXiv:2312.15558 [math.AP], 2023.                                           

2. Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise.
     K. Yamazaki, arXiv:2308.09692 [math.AP], 2023. 

3.  Another remark on the global regularity issue of the Hall-magnetohydrodynamics system.
     M. M. Rahman* and K. Yamazaki, arXiv:2302.03636 [math.AP], 2023. 

4.  Non-uniqueness in law of transport-diffusion equation forced by random noise.
     U. Koley and K. Yamazaki, arXiv:2203.13456 [math.AP], 2022. 

5.  A remark on the global well-posedness of a modified critical quasi-geostrophic equation.
     K. Yamazaki, arXiv:1006.0253 [math.AP], 2010.

Ph.D. Thesis

1.  On the existence and smoothness problem of the magnetohydrodynamics system.[pdf]
     K. Yamazaki, Ph.D. Thesis, Oklahoma State University, 2014.