On dynamics of fluids in meteorology

Lukáš Poul

Displaying similar documents to “On dynamics of fluids in meteorology”

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

Sébastien Novo, Antonín Novotný (2005)

Applications of Mathematics

Similarity:

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.

Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions

Antonín Novotný, Milan Pokorný (2011)

Applications of Mathematics

Similarity:

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law $p (ϱ, ϑ) \sim ϱ^{γ} + ϱ ϑ$ if $γ > 1$ and $p (ϱ, ϑ) \sim ϱ {ln}^{α} (1 + ϱ) + ϱ ϑ$ if $γ = 1$ , $α > 0$ , depending on the model for the heat flux.

On weak solutions of steady Navier-Stokes equations for monatomic gas

Jan Březina, Antonín Novotný (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We use $L^{\infty}$ estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant $γ > \frac{1}{3} (1 + \sqrt{13}) \approx 1.53$ for the flows powered by volume non-potential forces and with $γ > \frac{1}{8} (3 + \sqrt{41}) \approx 1.175$ for the flows powered by potential forces and arbitrary non-volume forces. According to our...

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

Petra Pecharová, Milan Pokorný (2010)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...