Gasdynamic regularity: some classifying geometrical remarks.
Generic solvability for the 3-D Navier-Stokes equations with nonregular force.
Global existence and uniqueness of strong solutions for the magnetohydrodynamic equations.
Global existence for a one-dimensional model in gas dynamics
We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.
Global existence of 2D slightly compressible viscous magneto-fluid motion.
Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid
Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.
Global solution of viscous compressible barotropic multipolar gas in a finite channel with nonzero input and output
The paper contains the proof of global existence of weak solutions of the viscous compressible barotropic gas for the initial-boundary value problem in a finite channel.
Global solution to the ideal compressible heat conductive multipolar fluid
Global solution to the isothermal compressible bipolar fluid in a finite channel with nonzero input and output
The paper contains the proof of global existence of weak solutions viscous compressible isothermal bipolar fluid of initial boundary value in a finite channel.
Global solutions of multidimensional approximate Navier-Stokes equations of a viscous gas.
Global solutions of quasilinear systems of Klein–Gordon equations in 3D
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
Global solutions of the Cauchy problem for a viscous polytropic ideal gas
Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media
We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing...
Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...
Global weak solvability to the regularized viscous compressible heat conductive flow
The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.