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In this paper, we investigate the global existence of weak solutions to 3-D inhomogeneous incompressible MHD equations with variable viscosity and resistivity, which is sufficiently close to $1$ in $L^\infty(\mathbb{R}^3),$ provided that…

Analysis of PDEs · Mathematics 2025-03-04 Hammadi Abidi , Guilong Gui , Ping Zhang

We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size…

Analysis of PDEs · Mathematics 2017-08-15 Van-Sang Ngo

In this paper, we construct a class global large solution to the 3D incompressible micropolar fluid system. Precisely speaking, by choosing a special initial data which can be arbitrarily large in $\dot{B}^{-1}_{\infty,\infty}$, the system…

Analysis of PDEs · Mathematics 2020-06-03 Jinlu Li , Weipeng Zhu

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space under some admissible condition. The result…

Analysis of PDEs · Mathematics 2023-10-17 Yuan Cai , Bin Han , Na Zhao

In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…

Analysis of PDEs · Mathematics 2024-08-15 Xiaoping Zhai , Shunhang Zhang

The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field.…

Analysis of PDEs · Mathematics 2011-08-30 Xiaoli Li , Ning Su , Dehua Wang

We consider the homogeneous Landau equation in $\mathbb{R}^3$ with Coulomb potential and initial data in polynomially weighted $L^{3/2}$. We show that there exists a smooth solution that is bounded for all positive times. The proof is based…

Analysis of PDEs · Mathematics 2025-05-09 William Golding , Maria Gualdani , Amélie Loher

In this paper we study the initial-boundary value problem for the magnetohydrodynamic system in three dimensional exterior domain. We show an existence theorem of global in time strong solution for small initial data and we also show its…

Analysis of PDEs · Mathematics 2016-09-07 Norikazu Yamaguchi

In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum…

Analysis of PDEs · Mathematics 2018-06-07 Edriss S. Titi , Saber Trabelsi

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows, we prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large…

Analysis of PDEs · Mathematics 2022-12-28 Canze Zhu , Qiang Tao

This paper studies the global existence of classical solutions to the two-dimensional incompressible magneto-hydrodynamical (MHD) system with only magnetic diffusion on the periodic domain. The approach is based on a time-weighted energy…

Analysis of PDEs · Mathematics 2018-08-29 Yi Zhou , Yi Zhu

The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the…

Analysis of PDEs · Mathematics 2022-08-10 Yazhou Chen , Yunkun Chen , Xue Wang

In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure: $u_0=u_0^r e_r+\ut_0 e_\theta+u_0^z e_z, ~b_0=b_0^\theta e_\theta.$ We prove that, this system is global well-posed…

Analysis of PDEs · Mathematics 2017-05-22 Yanlin Liu

In this note we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.

Analysis of PDEs · Mathematics 2012-07-19 Pavlo O. Kasyanov , Luisa Toscano , Nina V. Zadoianchuk

This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in…

Analysis of PDEs · Mathematics 2011-10-28 Boris Haspot

This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…

Analysis of PDEs · Mathematics 2017-11-17 Zhong Tan , Yanjin Wang

We study the Cauchy problem for generalized electron magnetohydrodynamics (EMHD). We establish the local existence and uniqueness of solutions in critical Sobolev spaces, as well as global existence and uniqueness for small initial data. In…

Analysis of PDEs · Mathematics 2026-03-19 Chao Wu

In this paper, we study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the…

Analysis of PDEs · Mathematics 2018-03-16 Dongyi Wei , Zhifei Zhang

We prove the global-in-time existence of H^2 solutions of the equations of compressible magnetohydrodynamics with zero magnetic resistivity in three space dimensions. Initial data are taken to be small in H^2 modulo a constant state and…

Analysis of PDEs · Mathematics 2020-11-16 Anthony Suen

We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.

Analysis of PDEs · Mathematics 2016-06-02 Michael Feischl , Thanh Tran