Research
Refereed Publications
The refereed publications are divided into three sections of
(a) Stochastic analysis in PDE, (b) Harmonic analysis in PDE, (c) 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). At the end, there is (d) Posted only on ArXiv (submitted or unsubmitted) and (e) Ph.D. Thesis.
(a) Stochastic analysis in PDE
Approximating three-dimensional magnetohydrodynamics system forced by space-time white noise.
K. Yamazaki, J. Differential Equations, 402 (2024), pp. 35--179. Its pre-print also available at arXiv:2002.12732 [math.AP].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].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].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.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. (2024), pp. 794--855. https://doi.org/10.1007/s40072-023-00293-x. Its pre-print also available at arXiv:2104.10294 [math.PR].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].Non-uniqueness in law for the Boussinesq system forced by random noise.
K. Yamazaki, Calc. Var. Partial Differential Equations, 61 (2022), pp. 1--65. https://doi.org/10.1007/s00526-022-02285-6. Its pre-print also available at arXiv:2101.05411 [math.AP]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].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].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), pp. 1--52. https://doi.org/10.1007/s00030-022-00753-8.Strong Feller property of the magnetohydrodynamics system forced by space-time white noise. [pdf]
K. Yamazaki, Nonlinearity, 34 (2021), pp. 1--91. https://doi.org/10.1088/1361-6544/abfae7.Boussinesq system with partial viscous diffusion or partial thermal diffusion forced by a random noise. [pdf]
K. Yamazaki, Appl. Math. Optim., (2021), pp. 1--38 https://doi.org/10.1007/s00245-021-09756-w.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.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.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.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.
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.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.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.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.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.
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.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.Exponential convergence of the stochastic micropolar and magneto-micropolar fluid systems. [pdf]
K. Yamazaki, Commun. Stoch. Anal., 10 (2016), pp. 271--295.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.Ergodicity of the two-dimensional magnetic Benard problem. [pdf]
K. Yamazaki, Electron. J. Differential Equations, 2016 (2016), pp. 1--24.Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system. [pdf]
K. Yamazaki, Adv. Differential Equations, 21 (2016), pp. 1085--1116.Global martingale solution for the stochastic Boussinesq system with zero dissipation. [pdf]
K. Yamazaki, Stoch. Anal. Appl., 34 (2016), pp. 404--426.
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]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.
(b) Harmonic analysis in PDE
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.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]On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation. [pdf]
A. Larios and K. Yamazaki, Phys. D, 411 (2020), 132560.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.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.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.Global regularity of logarithmically supercritical MHD system with improved logarithmic powers. [pdf]
K. Yamazaki, Dyn. Partial Differ. Equ., 15 (2018), pp. 147--173.Horizontal Biot-Savart law in general dimension and an application to the 4D magneto-hydrodynamics. [pdf]
K. Yamazaki, Differential Integral Equations, 31, 3/4 (2018), pp. 301--328.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.Global regularity of generalized magnetic Benard problem. [pdf]
K. Yamazaki, Math. Methods Appl. Sci., 40 (2017), pp. 2013--2033, doi: 10.1002/mma.4116.Regularity results on the Leray-alpha magnetohydrodynamics systems. [pdf]
D. KC* and K. Yamazaki, Nonlinear Anal. Real World Appl., 32 (2016), pp. 178--197.Regularity criteria of the 4D Navier-Stokes equations involving two velocity field components. [pdf]
K. Yamazaki, Commun. Math. Sci., 14 (2016), pp. 2229--2252.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.A remark on the two-dimensional magnetohydrodynamics-alpha system. [pdf]
K. Yamazaki, J. Math. Fluid Mech., 18 (2016), pp. 609--623.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.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.On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces. [pdf]
K. Yamazaki, Bull. Sci. Math., 140 (2016), pp. 575--614.Global regularity of N-dimensional generalized MHD system with anisotropic dissipation and diffusion. [pdf]
K. Yamazaki, Nonlinear Anal., 122 (2015), pp. 176--191.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.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.(N-1) velocity components condition for the generalized MHD system in N-dimension. [pdf]
K. Yamazaki, Kinet. Relat. Models, 7 (2014), pp. 779--792.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.Component reduction for regularity criteria of the three-dimensional magnetohydrodynamics systems. [pdf]
K. Yamazaki, Electron. J. Differential Equations, 2014, 98 (2014), pp. 1--18.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.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).On the global regularity of two-dimensional generalized magnetohydrodynamics system. [pdf]
K. Yamazaki, J. Math. Anal. Appl., 416 (2014), pp. 99--111.On the global regularity of N-dimensional generalized Boussinesq system. [pdf]
K. Yamazaki, Appl. Math., 60 (2015), pp. 109--133.Global regularity of logarithmically supercritical MHD system with zero diffusivity. [pdf]
K. Yamazaki, Appl. Math. Lett., 29 (2014), pp. 46--51.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.On the global well-posedness of N-dimensional generalized MHD system in anisotropic spaces.[pdf]
K. Yamazaki, Adv. Differential Equations, 19, 3-4 (2014), pp. 201--224.Remarks on the global regularity of two-dimensional magnetohydrodynamics system with zero dissipation. [pdf]
K. Yamazaki, Nonlinear Anal., 94 (2014), pp. 194--205.Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems. [pdf]
K. Yamazaki, J. Math. Phys., 54, 011502 (2013).On the regularity criteria of a surface quasi-geostrophic equation. [pdf]
K. Yamazaki, Nonlinear Anal., 75 (2012), pp. 4950--4956.On the global regularity of generalized Leray-alpha type models. [pdf]
K. Yamazaki, Nonlinear Anal., 75 (2012), pp. 503--515.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.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.
(c) Mathematical Biology
Improved stability analysis on a partially diffusive model of the coronavirus disease of 2019.
R. Covington**, S. Patton**, E. Walker**, and K. Yamazaki, Discrete Contin. Dyn. Syst. Ser. B (2024), doi: 10.3934/dcdsb.2024071.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.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, pp. 1--27.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.Threshold dynamics of reaction-diffusion partial differential equations model of Ebola virus disease. [pdf]
K. Yamazaki, Int. J. Biomath., 11 (2018), 1850108, pp. 1--30. https://doi.org/10.1142/S1793524518501085.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.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.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.
(d) Posted only on ArXiv (submitted or unsubmitted)
Surface quasi-geostrophic equations forced by random noise: prescribed energy and non-unique Markov selections.
E. Walker** and K. Yamazaki, arXiv:2407.00920 [math.AP], 2024.Non-uniqueness in law of the surface quasi-geostrophic equations: the case of linear multiplicative noise.
K. Yamazaki, arXiv:2312.15558v2 [math.AP], 2023.Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise.
K. Yamazaki, arXiv:2308.09692 [math.AP], 2023.Another remark on the global regularity issue of the Hall-magnetohydrodynamics system.
M. M. Rahman* and K. Yamazaki, arXiv:2302.03636 [math.AP], 2023.Non-uniqueness in law of transport-diffusion equation forced by random noise.
U. Koley and K. Yamazaki, arXiv:2203.13456 [math.AP], 2022.A remark on the global well-posedness of a modified critical quasi-geostrophic equation.
K. Yamazaki, arXiv:1006.0253 [math.AP], 2010.
(e) Ph.D. Thesis
On the existence and smoothness problem of the magnetohydrodynamics system.[pdf]
K. Yamazaki, Ph.D. Thesis, Oklahoma State University, 2014.