Mark Steinhauer

On Analysis of Steady Flows of Fluids with Shear-Dependent Viscosity Based on the Lipschitz Truncation Method

We deal with a system of partial differential equations describing a steady motion of an incompressible fluid with shear-dependent viscosity and present a new global existence result for

Everywhere α-estimates for a class of nonlinear elliptic systems with critical growth

p>\frac{2d}{d+2}

On Uniqueness- and Regularity Criteria for the Navier-Stokes Equations

. Here p is the coercivity parameter of the nonlinear elliptic operator related to the stress tensor and d is the dimension of the space. Lipschitz test functions, a subtle splitting of the level sets of the maximal functions for the velocity gradients, and a decomposition of the pressure are incorporated to obtain almost everywhere convergence of the velocity gradients.

On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications

Abstract. We obtain everywhere 𝒞α-regularity for vector solutions to a class of nonlinear elliptic systems whose principal part is the Euler operator to a variational integral ∫F(u,∇u)dx

An existence result for fluids with shear dependent viscosity — Steady flows

{\int F(u,\nabla u)\, dx}

The Dirichlet problem for steady viscous compressible flow in three dimensions

with quadratic growth in ∇u

L p -Estimates for the Navier–Stokes Equations for Steady Compressible Flow

{\nabla u}

The Dirichlet Problem for Viscous Compressible Isothermal Navier–Stokes Equations in Two Dimensions

and which satisfies a generalized splitting condition that cover the case F(u,∇u):=∑ i Q i ,

On Stationary Solutions for 2-D Viscous Compressible Isothermal Navier–Stokes Equations

{F(u,\nabla u):= \sum _i Q_i},\vspace*{-2.27621pt}

On existence of a classical solution to a generalized Kelvin–Voigt model

where Q i :=∑ αβ A i αβ (u,∇u)∇u α ·∇u β