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arXiv · 1302.2590

High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws

Stéphane Junca
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Abstract

The article first studies the propagation of well prepared high frequency waves with small amplitude $\eps$ near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating solutions are used to highlight a conjecture of Lions, Perthame, Tadmor, (1994), about the maximal regularizing effect for nonlinear conservation laws. For this purpose, a new definition of nonlinear flux is stated and compared to classical definitions. Then it is proved that the smoothness expected in Sobolev spaces cannot be exceeded.

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Stéphane Junca. 2013-02-11. High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws. https://arxiv.org/abs/1302.2590

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