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## About the shock formation in multi-dimensional scalar conservation laws

Denis Serre
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• PersonId : 1029085

#### Abstract

We establish a space-time integral estimate of the difference of solutions of non-degenerate scalar conservation laws. It is valid over the maximal domain $(0,T_{\rm max})\times\R^d$ in which the solutions are shock-free, and it fails beyond $T_{\rm max}$. When comparing a solution with its shifts, we deduce a Besov-like estimate at the development of its first singularity.

### Dates and versions

ensl-03967004 , version 1 (01-02-2023)

### Identifiers

• HAL Id : ensl-03967004 , version 1

### Cite

Denis Serre. About the shock formation in multi-dimensional scalar conservation laws. 2023. ⟨ensl-03967004⟩

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