On existence and regularity of solutions  to a class of generalized stationary Stokes problem

Nguyen Duc Huy; Jana Stará

Displaying similar documents to “On existence and regularity of solutions to a class of generalized stationary Stokes problem”

On a generalized Stokes problem

Václav Mácha (2011)

Open Mathematics

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We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.

A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid

Sébastien Novo, Antonín Novotný (2005)

Applications of Mathematics

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For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.

Steady compressible Navier-Stokes-Fourier system in two space dimensions

Petra Pecharová, Milan Pokorný (2010)

Commentationes Mathematicae Universitatis Carolinae

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We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation $p (ρ, θ) \sim ρ^{γ} + ρ θ$ , where $ρ$ is the density and $θ$ is the temperature. For $γ > 2$ , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness...

Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods

Basil Nicolaenko, Alex Mahalov, Timofey Shilkin (2006-2007)

Séminaire Équations aux dérivées partielles

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We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space $L^{3} (R^{3})$ . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally $L^{3}$ . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.