Strichartz type estimates for fractional heat equations

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dc.creatorZhai, Zhichun
dc.date2009-04-21
dc.date.accessioned2026-07-07T13:06:52Z
dc.date.available2026-07-07T13:06:52Z
dc.descriptionWe obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-Littlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing $ L^{\infty}_{x}(\mathbb{R}^{n})$ by $BMO_{x}(\mathbb{R}^{n})$ and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with either Besov spaces or Sobolev spaces. Moreover, we establish the Strichartz estimates for the fractional heat equations with a time dependent potential of an appropriate integrability. As an application, we prove the global existence and uniqueness of regular solutions in spatial variables for the generalized Navier-Stokes system with $L^{r}(\mathbb{R}^{n})$ data.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0904.3259
dc.identifierhttp://arxiv.org/abs/0904.3259
dc.identifierJ. Math. Anal. Appl. 356 (2009) 642-658
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227917
dc.subjectAnalysis of PDEs
dc.titleStrichartz type estimates for fractional heat equations
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