58 research outputs found
The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation
Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
summary: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, a so called energy inequality is derived. The inequality is independent on the regularization used
The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid
MODELING OF FLOWS THROUGH A CHANNEL BY THE NAVIER–STOKES VARIATIONAL INEQUALITIES
We deal with a mathematical model of a flow of an incompressible Newtonian fluid through a channel with an artificial boundary condition on the outflow. We explain how several artificial boundary conditions formally follow from appropriate variational formulations and the wayone expresses the dynamic stress tensor. As the boundary condition of the “do nothing”–type, that is predominantly considered to be the most appropriate from the physical point of view, does not enable one to derive an energy inequality, we explain how this problem can be overcome by using variational inequalities. We derive a priori estimates, which are the core of the proofs, and present theorems on the existence of solutions in the unsteady and steady cases
Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains
We consider the compressible (barotropic) Navier-Stokes system on
time-dependent domains, supplemented with slip boundary conditions. Our
approach is based on penalization of the boundary behaviour, viscosity, and the
pressure in the weak formulation. Global-in-time weak solutions are obtained
Regularity criteria for weak solutions to the Navier–Stokes equations based on spectral projections of vorticity
On the regularity up to the boundary in the theory of the Navier–Stokes equations with generalized impermeability conditions
Local in time strong solvability of the non-steady Navier–Stokes equations with Navier's boundary condition and the question of the inviscid limit
The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions
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