Hölder continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions

DOI10.1007/s00030-017-0449-7zbMath1375.35065arXiv1610.00229OpenAlexW2529789061MaRDI QIDQ2410992

Jakub Tichý, Václav Mácha

Publication date: 20 October 2017

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.00229

zbMATH Keywords

generalized Newtonian fluidregularity up to the boundary

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items

Multiple sign-changing solutions for nonlinear fractional Kirchhoff equations, Some existence results on a class of generalized quasilinear Schrödinger equations with Choquard type, Time regularity for parabolic \(p(x, t)\)-Laplacian system depending on the symmetric gradient, Positive and negative solutions for the nonlinear fractional Kirchhoff equation in \(\mathbb{R}^N \), Hölder continuity of solutions for unsteady generalized Navier-Stokes equations with \(p(x,t)\)-power law in 2D, Concentration behavior of nonlinear Hartree-type equation with almost mass critical exponent

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differentiability of the solution operator and the dimension of the attractor for certain power--law fluids
• Navier-Stokes equations with first order boundary conditions
• Optimal control of planar flow of incompressible non-Newtonian fluids
• Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities
• Boundary regularity of flows under perfect slip boundary conditions
• Regularity of flows of a non-Newtonian fluid subject to Dirichlet boundary conditions
• Optimal Control of Shear-Thickening Flows
• Optimal Control of Shear-Thinning Fluids
• Weakly Differentiable Functions
• On the regularity of weak solutions to parabolic systems in two spatial dimensions
• \(C^{1,\alpha}\)-solutions to a class of nonlinear fluids in two dimensions-stationary Dirichlet problem