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arXiv · 2009.01049

Well-posedness and parabolic smoothing effect for higher order Schr\"odinger type equations with constant coefficients

Tomoyuki Tanaka·Kotaro Tsugawa
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Abstract

We consider the Cauchy problem of a class of higher order Schr\"odinger type equations with constant coefficients. By employing the energy inequality, we show the $L^2$ well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property.

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Tomoyuki Tanaka, Kotaro Tsugawa. 2020-09-02. Well-posedness and parabolic smoothing effect for higher order Schr\"odinger type equations with constant coefficients. https://arxiv.org/abs/2009.01049

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