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

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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.

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

Antonín Novotný, Milan Pokorný (2011)

Applications of Mathematics

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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

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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

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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 pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Martin Lanzendörfer, Jan Stebel (2011)

Applications of Mathematics

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We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results. ...