On the regularity of weak solutions to parabolic systems in two spatial dimensions

DOI10.1080/03605309808821382zbMath0937.35020OpenAlexW1964927252MaRDI QIDQ4220027

Oldřich John, A.I.Kozhanov

Publication date: 3 May 2000

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309808821382

zbMATH Keywords

difference estimatesnonlinear parabolic system with nonsmooth coefficients

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Second-order parabolic systems (35K40)

Related Items (14)

Analysis of the adiabatic piston problem via methods of continuum mechanics ⋮ Hölder continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions ⋮ Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange ⋮ Finite time blowup for parabolic systems in two dimensions ⋮ Local and global existence of strong solutions to large cross diffusion systems ⋮ Existence of strong and nontrivial solutions to strongly coupled elliptic systems ⋮ Regularity of flows of a non-Newtonian fluid subject to Dirichlet boundary conditions ⋮ Uniqueness and regularity of unbounded weak solutions to a class of cross diffusion systems ⋮ Weighted Gagliardo–Nirenberg Inequalities Involving BMO Norms and Solvability of Strongly Coupled Parabolic Systems ⋮ Existence of regular solutions for a certain type of non-Newtonian fluids ⋮ Regularity of BMO weak solutions to nonlinear parabolic systems via homotopy ⋮ Parabolic Systems with Polynomial Growth and Regularity ⋮ On a Quasilinear Parabolic Curl System Motivated by Time Evolution of Meissner States of Superconductors ⋮ Second order parabolic systems, optimal regularity, and singular sets of solutions

Cites Work

• On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions
• On the partial regularity of weak solutions on nonlinear parabolic systems
• Partial regularity for the solutions to nonlinear parabolic systems
• Regularity of Solutions for Some Quasilinear Parabolic Systems

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