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

Basil Nicolaenko; Alex Mahalov; Timofey Shilkin

Displaying similar documents to “Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods”

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...

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

Nguyen Duc Huy, Jana Stará (2006)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient $\nabla p$ is replaced by a linear operator of first order.

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

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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 $𝕧$ .