Related papers: Global solutions to planar magnetohydrodynamic equ…
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…
We study the evolution of a compressible fluid surrounded by vacuum and introduce a new symmetrization in Lagrangian coordinates that allows us to encompass both relativistic and non-relativistic fluid flows. The problem under consideration…
In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic (MHD) flow with no-slip boundary condition of velocity…
By observing a new relation between the magnetic pressure and the hydrodynamic pressure, global existence of classical solution to the full perfect MHD equations with large data is established, in particular including the case when all the…
An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
We consider the complete system of equations governing the motion of a general compressible, viscous, electrically and heat conductive fluid driven by non-conservative boundary conditions. We show the existence of a bounded absorbing set in…
The concept of magnetic connections is extended to non-ideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall and…
In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…
When the vaccum is allowed, if the global existence and uniqueness of strong solutions to three dimensional incompressible inhomogeneous magnetohydrodynamic equations holds true or not has always been a challenging open problem, even for…
We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the…
We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…
This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by…
We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…
In this paper, we consider the Cauchy problem to the planar magnetohydrodynamics (MHD) system with both constant viscosity and constant resistivity but without heat conductivity. Global well-posedness of strong solutions in the presence of…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…
We investigate the Cauchy problem to the compressible planar non-resistive magnetohydrodynamic equations with zero heat conduction. The global existence of strong solutions to such a model has been established by Li and Li (J. Differential…