On Regularity of the Time Derivative for Degenerate Parabolic Systems

DOI10.1137/141000725zbMath1325.35108arXiv1501.04876OpenAlexW1933616847MaRDI QIDQ3195480

Jens Frehse, Sebastian Schwarzacher

Publication date: 19 October 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.04876

zbMATH Keywords

regularitynon-Newtonian fluidsdegenerate parabolic systems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

Related Items (13)

Evolutionary, symmetric \(p\)-Laplacian. Interior regularity of time derivatives and its consequences ⋮ Regularity results for two standard models in elasto-perfect-plasticity theory with hardening ⋮ Regularity for parabolic systems of Uhlenbeck type with Orlicz growth ⋮ Higher differentiability for solutions of stationary p‐Stokes systems ⋮ Temporal regularity of symmetric stochastic \(p\)-Stokes systems ⋮ Time regularity of generalized Navier-Stokes equation with $p(x,t)$-power law ⋮ Time regularity for parabolic \(p(x, t)\)-Laplacian system depending on the symmetric gradient ⋮ Parabolic p-Laplacian revisited: Global regularity and fractional smoothness ⋮ Second-order regularity for parabolic \(p\)-Laplace problems ⋮ A revision of results for standard models in elasto-perfect-plasticity theory ⋮ Interior regularity of space derivatives to an evolutionary, symmetric \(\varphi\)-Laplacian ⋮ Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth ⋮ Stability and distributed control of degenerate diffusion equations

Cites Work

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• Linear potentials in nonlinear potential theory
• \(L^q\) theory for a generalized Stokes system
• Hölder-Zygmund estimates for degenerate parabolic systems
• The Wolff gradient bound for degenerate parabolic equations
• Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems
• Local Hölder regularity of gradients for evolutional \(p\)-Laplacian systems
• On uniqueness and time regularity of flows of power-law like non-Newtonian fluids
• Fractional differentiability for the stress velocities to the solution of the Prandtl-Reuss problem
• Hölder estimates for nonlinear degenerate parabolic sytems.
• Projections onto gradient fields and $L^{p}$-estimates for degenerated elliptic operators
• Fractional estimates for non-differentiable elliptic systems with general growth
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