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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
11/2003

Parabolic systems with nowhere smooth solutions

Stefan Müller, Marc Oliver Rieger and Vladimír Šverák

Abstract

We construct smooth $2\times 2$ parabolic systems with smooth initial data and $C^\alpha$ right hand side which admit solutions that are nowhere $C^1$. The elliptic part is in variational form and the corresponding energy $\phi$ is strongly quasiconvex and in particular satisfies a uniform Legendre-Hadamard (or strong ellipticity) condition.

Received:
08.02.03
Published:
08.02.03
MSC Codes:
35B65, 35K55
Keywords:
regularity, parabolic systems, convex integration

Related publications

inJournal
2005 Repository Open Access
Stefan Müller, Marc Oliver Rieger and Vladimír Šverák

Parabolic systems with nowhere smooth solutions

In: Archive for rational mechanics and analysis, 177 (2005) 1, pp. 1-20