Self-Similar Solutions for Nonlinear Schrodinger Equations

Changxing Miao; Bo Zhang; Xiaoyi Zhang

doi:10.4310/MAA.2003.v10.n1.a7

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Self-Similar Solutions for Nonlinear Schrodinger Equations

Journal article

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Self-Similar Solutions for Nonlinear Schrodinger Equations

Changxing Miao, Bo Zhang and Xiaoyi Zhang

Methods and applications of analysis, Vol.10(no. 1), pp.119-136

2003

DOI: 10.4310/MAA.2003.v10.n1.a7

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Abstract

In this paper we study self-similar solutions for nonlinear Schrodinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrodinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in Besov spaces, employing the mean difference characterization and multiplication in Besov spaces. These new global solutions to nonlinear Schrodinger equations with small data admit a class of self-similar solutions. Our results improve and extend the well-known results of Planchon [18], Cazenave and Weissler [4, 5] and Ribaud and Youssfi [20].

Details

Title: Subtitle: Self-Similar Solutions for Nonlinear Schrodinger Equations
Creators: Changxing Miao
Bo Zhang
Xiaoyi Zhang
Resource Type: Journal article
Publication Details: Methods and applications of analysis, Vol.10(no. 1), pp.119-136
DOI: 10.4310/MAA.2003.v10.n1.a7
ISSN: 1073-2772
eISSN: 1945-0001
Publisher: International Press of Boston
Date published: 2003
Academic Unit: Mathematics
Record Identifier: 9984242413802771

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