Related papers: Well-posedness for magnetoviscoelastic fluids in 3…
This paper investigates the existence and uniqueness of local strong solutions to the three-dimensional compressible magnetohydrodynamic (MHD) equations with density-dependent viscosities in an exterior domain. The system models the…
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magneto-hydrodynamical system with initial data close enough to the equilibrium state, $(e_3,0).$ Compared with the the previous works…
We study the local existence of solutions to the magnetohydrodynamics (MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the $L^p-L^q$ class with inhomogeneous boundary conditions. The…
In this article, we prove the local well-posedness, for arbitrary initial data with certain regularity assumptions, of the equations of a Viscoelastic Fluid of Johnson-Segalman type with a free surface. More general constitutive laws can be…
We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial data in critical Besov spaces, which generalize the result in [10]. Meanwhile , we analyze the…
We show convergence of solutions to equilibria for quasilinear and fully nonlinear parabolic evolution equations in situations where the set of equilibria is non-discrete, but forms a finite-dimensional $C^1$-manifold which is normally…
We study the local and global wellposedness of a full system of Magneto-Hydro-Dynamic equations. The system is a coupling of the forced (Lorentz force) incompressible Navier-Stokes equations with the Maxwell equations through Ohm's law for…
We study the global stability of large solutions to the compressible isentropic magnetohydrodynamic equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the solutions converge to an…
We prove that for any closed manifold of dimension 3 or greater that there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the…
We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…
We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global…
We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions.
We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p =…
We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
We prove the local well-posedness of a basic model for relaxational fluid vesicle dynamics by a contraction mapping argument. Our approach is based on the maximal $L_p$-regularity of the model's linearization.
In this paper we are concerned with $L^p$-maximal parabolic regularity for abstract nonautonomous parabolic systems and their quasilinear counterpart in negative Sobolev spaces incorporating mixed boundary conditions. Our results are…