Displaying similar documents to “A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum”

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 ) ∼ 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...

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 ) ∼ ϱ γ + ϱ ϑ if γ > 1 and p ( ϱ , ϑ ) ∼ ϱ ln α ( 1 + ϱ ) + ϱ ϑ if γ = 1 , α > 0 , depending on the model for the heat flux.

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. ...

Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class L ∞ ( 0 , T , L 3 ( Ω ) 3 )

Zdeněk Skalák (2003)

Applications of Mathematics

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We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution 𝐮 belongs to L ∞ ( 0 , T , L 3 ( Ω ) 3 ) , then the set of all possible singular points of 𝐮 in Ω is at most finite at every time t 0 ∈ ( 0 , T ) .