A necessary condition for $H^\infty$ well-posedness of p-evolution equations

A. Ascanelli; C. Boiti; L. Zanghirati

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arXiv · 1406.6183

A necessary condition for $H^\infty$ well-posedness of p-evolution equations

A. Ascanelli·C. Boiti·L. Zanghirati

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Abstract

We consider p-evolution equations, for $p\geq2$, with complex valued coefficients. We prove that a necessary condition for $H^\infty$ well-posedness of the associated Cauchy problem is that the imaginary part of the coefficient of the subprincipal part (in the sense of Petrowski) satisfies a decay estimate as x goes to infinity.

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A. Ascanelli, C. Boiti, L. Zanghirati. 2014-06-24. A necessary condition for $H^\infty$ well-posedness of p-evolution equations. https://arxiv.org/abs/1406.6183

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