Self-Similar Solutions for Nonlinear Schrodinger Equations
Miao, Changxing ; Zhang, Bo ; Zhang, Xiaoyi
Methods Appl. Anal., Tome 10 (2003) no. 3, p. 119-136 / Harvested from Project Euclid
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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].
Publié le : 2003-03-14
Classification:  
@article{1118943105,
     author = {Miao, Changxing and Zhang, Bo and Zhang, Xiaoyi},
     title = {Self-Similar Solutions for Nonlinear Schrodinger Equations},
     journal = {Methods Appl. Anal.},
     volume = {10},
     number = {3},
     year = {2003},
     pages = { 119-136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1118943105}
}

Miao, Changxing; Zhang, Bo; Zhang, Xiaoyi. Self-Similar Solutions for Nonlinear Schrodinger Equations. Methods Appl. Anal., Tome 10 (2003) no. 3, pp.  119-136. http://gdmltest.u-ga.fr/item/1118943105/