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

Sébastien Novo; Antonín Novotný

Displaying similar documents to “A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid”

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. ...

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.

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 dynamics of fluids in meteorology

Lukáš Poul (2008)

Open Mathematics

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We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl and others in the series of works on compressible, viscous and heat conducting fluids.

A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum

Jens Frehse, Sonja Goj, Josef Málek (2005)

Applications of Mathematics

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We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities $ρ_{i}$ of the fluids and their velocity fields $u^{(i)}$ are prescribed at infinity: $ρ_{i} |_{\infty} = ρ_{i \infty} > 0$ , $u^{(i)} |_{\infty} = 0$ . Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely $ρ_{i} \equiv ρ_{i \infty}$ , $u^{(i)} \equiv 0$ , $i = 1, 2$ .