## A necessary condition for $$H^\infty$$ well-posedness of $$p$$-evolution equations.(English)Zbl 1375.35090

Summary: 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 $$|x|\to+\infty$$.

### MSC:

 35G10 Initial value problems for linear higher-order PDEs 35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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