PROPOSED RESEARCH
PROPOSED RESEARCH
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Contribution 1 (BC1)
Well-posedness of 3D Boussinesq mild solutions in large adapted critical spaces.
In this research project we are interested in the existence of a certain class of mild solutions for the 3D incompressible Boussinesq system which is based in the Navier-Stokes equations
Researchers: Diego Chamorro, Fernando Cortez, Oscar Jarrín, Naraya Narváez.
Contribution 2 (BC2)
Solitary waves for the Zakharov/Craig-Sulem formulation to model water waves.
This project seeks the study for the solitons dynamics under a slowly varying bottom for the 3-dimensional water waves system.
Researchers: María E. Martínez, Claudio Muñoz, Frédéric Rousset.
Contribution 3 (BC3)
Geometrical description and properties of general solitonic structures in Kadomtsev - Petviashvili models.
In this proposal part, we want to further advance in the geometrical description and properties of general solitonic structures or more generally N-solitons.
Researchers: Gong Chen, Francisco Alegría, Claudio Muñoz, Felipe Poblete, Matthiew Paillard, Benjamín Tardy.
See recent work "On uniqueness of KP soliton structures".
Contribution 4 (BC4)
The UVic Earth Model of Intermediate Complexity (EMIC).
We seek for a rigorous framework or suitable modification under which the model has a well-posed description.
Researchers: Oscar Jarrín, Claudio Muñoz
Contribution 5 (BC5)
Stiff fluids in FLRW spacetimes.
The purpose of this subproject is to explore stiff-fluids using virial techniques to obtain rigorous insights about the cosmological dynamics.
Researchers: Diego Chamorro, Claudio Muñoz, Jessica Trespalacios.
Contribution 6 (BC6)
A fluid-structure system.
The main purpose of this subproject is to study the vanishing limit problem for fluid-solid system.
Researchers: Diego Chamorro, Jiao He, Claudio Muñoz.
PREVIOUS JOINT RESEARCH WORKS
(1) D. Chamorro, and J. He, Regularity theory for the dissipative solutions of the magnetohy- drodynamic equations. SIAM J. Math. Anal. 53 (2021), no. 5, 5288–5321.
(2) D. Chamorro, O. Jarrín, and P-G. Lemarié-Rieusset, On the Kolmogorov dissipation law in a damped Navier-Stokes equation. J. Dynam. Differential Equations 33 (2021), no. 2, 1109–1134.
3) D. Chamorro, F. Cortez, J. He and O. Jarrín, On the local regularity theory for the magnetohydrodynamic equations. Doc. Math. 26 (2021), 125–148.
(4) D. Chamorro, O. Jarrín, and P.-G. Lemarié-Rieusset, Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces. Ann. Inst. H. Poincaré C Anal. Non Lin ́eaire 38 (2021), no. 3, 689–710.
(5) D. Chamorro, and J. He, On the partial regularity theory for the MHD equations. J. Math. Anal. Appl. 494 (2021), no. 1, Paper No. 124449, 38 pp.
(6) D. Chamorro, O. Jarrín, and P.-G. Lemarié-Rieusset, Frequency decay for Navier-Stokes stationary solutions, C. R. Math. Acad. Sci. Paris 357 (2019), no. 2, 175–179.
(7) D. Chamorro, and O. Jarrín, Fractional Laplacians, extension problems and Lie groups. C. R. Math. Acad. Sci. Paris 353 (2015), no. 6, 517–522.
(8) O. Jarrín, and M. F. Cortez, On decay properties and asymptotic behavior of solutions to a non-local perturbed KdV equation. Nonlinear Anal. 187 (2019), 365–396.
(9) O. Jarrín, and M. F. Cortez, Spatial behavior of solutions for a large class of non-local PDE’s arising from stratified flows. Differential Integral Equations 34 (2021), no. 9-10, 539–594.
(10) O. Jarrín, and M. F. Cortez, On the long-time behavior for a damped Navier-Stokes- Bardina model. Discrete Contin. Dyn. Syst. 42 (2022), no. 8, 3661–3707.
(11) A. J. Mendez, C. Muñoz, F. Poblete, and J. C. Pozo, On local energy decay for large solutions of the Zakharov-Kuznetsov equation. Comm. Partial Differential Equations 46 (2021), no. 8, 1440–1487.
(12) A. J. Mendez, C. Muñoz, F. Poblete, and J. C. Pozo, Long time asymptotics of large data in the Kadomtsev-Petviashvili models, preprint, arXiv:2101.08921, 2021.
(13) M. A. Alejo, M. F. Cortez, C. Kwak, and C. Muñoz, On the dynamics of zero-speed solutions for Camassa-Holm-type equations. Int. Math. Res. Not. IMRN 2021, no. 9, 6543–6585.
(14) C. Kwak, C. Muñoz, F. Poblete, and J. C. Pozo, The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space. J. Math. Pures Appl. (9) 127 (2019), 121–159.
(15) C. Muñoz, F. Poblete, and J. C. Pozo, Scattering in the energy space for Boussinesq equations. Comm. Math. Phys. 361 (2018), no. 1, 127–141.
(16) C. Muñoz, and J. Trespalacios, Global Existence and Long Time Behavior in Einstein-Belinski-Zakharov Soliton Spacetimes, preprint ArXiv 2023 https://arxiv.org/abs/2305. 01414.
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