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The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure

Jiří Neustupa — 2003

Applications of Mathematics

We assume that 𝕧 is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of 𝕧 near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of 𝕧 .

Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid

Jiří Neustupa — 1988

Aplikace matematiky

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 geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Jiří Neustupa — 2014

Mathematica Bohemica

We deal with a suitable weak solution ( 𝐯 , p ) to the Navier-Stokes equations in a domain Ω 3 . We refine the criterion for the local regularity of this solution at the point ( 𝐟 x 0 , t 0 ) , which uses the L 3 -norm of 𝐯 and the L 3 / 2 -norm of p in a shrinking backward parabolic neighbourhood of ( 𝐱 0 , t 0 ) . The refinement consists in the fact that only the values of 𝐯 , respectively p , in the exterior of a space-time paraboloid with vertex at ( 𝐱 0 , t 0 ) , respectively in a ”small” subset of this exterior, are considered. The consequence is that...

Global weak solvability to the regularized viscous compressible heat conductive flow

Jiří NeustupaAntonín Novotný — 1991

Applications of Mathematics

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.

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