On the local Smoothness of Solutions of the Navier-Stokes Equations

dc.creatorDong, Hongjie
dc.creatorDu, Dapeng
dc.date2005-02-05
dc.date.accessioned2026-07-07T05:16:43Z
dc.date.available2026-07-07T05:16:43Z
dc.descriptionWe consider the Cauchy problem for incompressible Navier-Stokes equations $u_t+u\nabla_xu-Δu+\nabla p=0, div u=0 in R^d \times R^+$ with initial data $a\in L^d(R^d)$, and study in some detail the smoothing effect of the equation. We prove that for $T<\infty$ and for any positive integers $n$ and $m$ we have $t^{m+n/2}D^m_tD^{n}_x u\in L^{d+2}(R^d\times (0,T))$, as long as the $\|u\|_{L^{d+2}_{x,t}(R^d\times (0,T))}$ stays finite.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0502104
dc.identifierhttp://arxiv.org/abs/math/0502104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74089
dc.subjectAnalysis of PDEs
dc.subject35Q30; 76D03; 76D05
dc.titleOn the local Smoothness of Solutions of the Navier-Stokes Equations
dc.typetext

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