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Parabolic systems with nowhere smooth solutions
Stefan Müller, Marc Oliver Rieger and Vladimír Šverák
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.