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

Jörg Wolf

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 ${u |}_{\partial B} = 0$ and ${lim}_{| x | \to \infty} {| x |}^{1 / 3} | u (x) | = 0$ uniformly. For slow flows the latter condition can be replaced by ${lim}_{| x | \to \infty} | u (x) | = 0$ uniformly. In particular, these results hold for the classical Navier-Stokes case.

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let $u$ be a weak solution of a quasilinear elliptic equation of the growth $p$ with a measure right hand term $μ$ . We estimate $u (z)$ at an interior point $z$ of the domain $Ω$ , or an irregular boundary point $z \in \partial Ω$ , in terms of a norm of $u$ , a nonlinear potential of $μ$ and the Wiener integral of $𝐑^{n} ∖ Ω$ . This quantifies the result on necessity of the Wiener criterion.

Displaying similar documents to “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 ”

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

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Displaying similar documents to “Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case $q = \frac{3 d}{d + 2}$ ”