Cauchy problem of nonlinear Schrödinger equation with Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$

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dc.creatorZhou, Yi
dc.date2007-01-18
dc.date2007-01-30
dc.date.accessioned2026-07-07T07:43:34Z
dc.date.available2026-07-07T07:43:34Z
dc.descriptionIn this paper, we consider in $R^n$ the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in $W^{s,p}$ for $\frac{2n}{n+1}<p<2$ and $s>n(1-\frac{1}{p})$. Moreover, we show that in one space dimension, the problem is locally well posed in $L^p$ for any $1<p<2$.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0701497
dc.identifierhttp://arxiv.org/abs/math/0701497
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122875
dc.subjectAnalysis of PDEs
dc.subject35Q35
dc.titleCauchy problem of nonlinear Schrödinger equation with Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$
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