Related papers: The three dimensional magneto-hydrostatic equation…
The equations of the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows are considered in a bounded domain. The viscosity coefficients and heat conductivity can depend on the temperature. A solution to…
We propose and analyze a new method for the unsteady incompressible magnetohydrodynamics equations on convex domains with hybrid approximations of both vector-valued and scalar-valued fields. The proposed method is convection-semirobust,…
In this paper a characteristics-based open boundary condition (CBC) is proposed for the magnetohydrodynamic (MHD) system of equations. The algorithm is carefully designed and implemented in the context of a high-order flux reconstruction…
This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated…
Several formulations of a local geometric measure-type condition are imposed on super-level sets of mild solutions to the homogeneous incompressible 3D magnetohydrodynamical system with bounded initial data to prevent finite-time…
We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish a priori estimate for solutions in the Lagrangian coordinates with…
In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.
In this paper, we study the existence of strong solutions to the two-phase magnetohydrodynamic equations in a bounded domain $\Omega\subseteq \mathbb{R}^3$. The fluids are incompressible, viscous, and resistive. The surface tension is…
We show, using the spectral Galerkin method together with compactness arguments, existence and uniqueness of the periodic strong solutions for the magnetohydrodynamics's type equations with inhomogeneous boundary conditions. Also, we study…
We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0,…
In this paper the boundary value problem for one class of the operator-differential equations of the third order on a semi-axis, where one of the boundary conditions is perturbed by some linear operator is researched. There are received…
The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,\bf{e_1})$ for…
In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors…
In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the…