On heat equations associated with fractional harmonic oscillators

Published 14 Oct 2022 in math.AP and math.FA | (2210.07691v1)

Abstract: We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator $e^{{-tH^{\beta}}$,} $t, \beta>0$, associated with the harmonic oscillator $H=-\Delta + |x|^2$. We then prove some local and global wellposedness results for nonlinear fractional heat equations.

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