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arXiv · 2210.07691

On heat equations associated with fractional harmonic oscillators

Divyang G. Bhimani·Ramesh Manna·Fabio Nicola·Sundaram Thangavelu·S. Ivan Trapasso
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Abstract

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

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Divyang G. Bhimani, Ramesh Manna, Fabio Nicola, Sundaram Thangavelu, S. Ivan Trapasso. 2022-10-14. On heat equations associated with fractional harmonic oscillators. https://arxiv.org/abs/2210.07691

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