dinger equations;global solutions;almost global solutions;regularity;"/> dinger equations;global solutions;almost global solutions;regularity;"/> Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations | Korea Science
Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 1,  2008, pp.101-108
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.1.101
Title & Authors
Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations
Zhao, Xiangqing; Cui, Shangbin;

Abstract
In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr$\small{\"{o}}$dinger equation: $\small{iu_t\;+\;{\Delta}u\;+\;{\mid}u{\mid}^{\alpha}u\;+\;a{\Sigma}_i^d\;u_{x_ix_ix_ix_i}}$ = 0, where a is real constant, 1 $\small{\leq}$ d < n is a integer is a positive constant, and x = $\small{(x_1,x_2,\cdots,x_n)\;\in\;R^n}$. For some admissible $\small{{\alpha}}$ we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.
Keywords
non-isotropic Schr$\small{\"{o}}$dinger equations;global solutions;almost global solutions;regularity;
Language
English
Cited by
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