Displaying similar documents to “Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions”

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...

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 ) .

On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity

Michael Bildhauer, Martin Fuchs (2012)

Commentationes Mathematicae Universitatis Carolinae

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On the complement of the unit disk B we consider solutions of the equations describing the stationary flow of an incompressible fluid with shear dependent viscosity. We show that the velocity field u is equal to zero provided u | ∂ B = 0 and lim | x | → ∞ | x | 1 / 3 | u ( x ) | = 0 uniformly. For slow flows the latter condition can be replaced by lim | x | → ∞ | u ( x ) | = 0 uniformly. In particular, these results hold for the classical Navier-Stokes case.

Boundary regularity of flows under perfect slip boundary conditions

Petr Kaplický, Jakub Tichý (2013)

Open Mathematics

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We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.