Related papers: Global regularity for solutions of magnetohydrodyn…
In this paper we are concerned with the global well-posedness of solutions to magnetohydrodynamics (MHD) boundary layer equations in analytic function spaces. When the initial data is a small perturbation around a selected profile, and such…
We are concerned with an initial boundary value problem for the compressible magnetohydrodynamic equations with viscosity depending on the density. It is show that for the initial density away from vacuum, the strong solution to the problem…
Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes…
Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is…
In to previous papers by the authors, classes of initial data to the three dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen…
In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known…
We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we…
This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness…
We study partial regularity of suitable weak solutions of the steady Hall magnetohydrodynamics equations in a domain $\Omega \subset \Bbb R^3$. In particular we prove that the set of possible singularities of the suitable weak solution has…
In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term.…
In this paper, we will show that solutions of the three-dimensional non-resistive and non-diffusive MHD-Boussinesq system are globally regular if the initial data is axisymmetric and the swirl components of the velocity and the magnetic…
We study the incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of…
Due to the absence of dissipation mechanism to the inviscid compressible systems, it is a challenging problem to prove their global solvability. In this paper, we are concerned with the initial-boundary value problem to the inviscid and…
We show at the PDE level that the monolithic parabolic regularization of the equations of ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfills the minimum entropy principle, and preserves the…
This paper is concerned with the stability and large-time behavior for 3D magneto-micropolar equations with horizontal dissipation. The global well-posedness of the aforementioned system is established, with the initial data and its…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
This paper is devoted to the study of the global existence of smooth solutions for the 3+1 dimensional Einstein-Klein-Gordon systems with a $U(1) \times \mathbb{R}$ isometry group for a class of regular Cauchy data. In our first paper…
Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the…
We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and…
This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Magnetohydrodynamic (MHD) equations with vacuum as far field density. We establish the global existence and uniqueness of strong solutions to…