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

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

Michael Bildhauer, Martin Fuchs (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case q = 3 d d + 2

Jörg Wolf (2007)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper we consider weak solutions 𝐮 : Ω → ℝ d to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain Ω ⊂ ℝ d ( d = 2 or d = 3 ). For the critical case q = 3 d d + 2 we prove the higher integrability of ∇ 𝐮 which forms the basis for applying the method of differences in order to get fractional differentiability of ∇ 𝐮 . From this we show the existence of second order weak derivatives of u .

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 ) ∼ 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.