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

Abstract

We consider p-evolution equations, for $p\ge 2$, 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.

References in corpus (2)

• Semilinear p-evolution equations in Sobolev spaces
• Weighted energy estimates for $p$-evolution equations

Cited by in corpus (1)

• Semilinear p-evolution equations in Sobolev spaces