Schr\"odinger ultrahyperbolic equations with singular coefficients

TL;DR

This paper studies the well-posedness of Schr"odinger ultrahyperbolic equations with singular coefficients, establishing results that extend classical smooth-coefficient theory to less regular cases.

Contribution

It proves $H^$ well-posedness for equations with singular, distributional coefficients, broadening the understanding of such PDEs beyond smooth cases.

Findings

Established $H^$ well-posedness under singular coefficients

Proved consistency with classical results for smooth coefficients

Extended PDE theory to less regular coefficient scenarios

Abstract

In this paper we investigate the Cauchy problem for Schr\"odinger ultrahyperbolic equations with singular (less than continuous) coefficients. We prove $H^\infty$ well-posedness in the very weak sense under suitable assumptions of the distributional structure of the coefficients and decay on the lower order terms. Consistency is proven with the classical $H^\infty$-results when the equation coefficients are smooth.