LOCAL WELLPOSEDNESS FOR THE 2+1-DIMENSIONAL MONOPOLE EQUATION

被引：10
|
作者：
Czubak, Magdalena [1 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
ANALYSIS & PDE | 2010年 / 3卷 / 02期
关键词：
monopole; null form; Coulomb gauge; wellposedness; NONLINEAR-WAVE EQUATIONS; YANG-MILLS EQUATIONS; NULL FORMS; EXISTENCE; REDUCTIONS; REGULARITY; DIMENSIONS; SYSTEMS;
D O I：
10.2140/apde.2010.3.151
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The space-time monopole equation on R(2+1) can be derived by a dimensional reduction of the antiselfdual Yang-Mills equations on R(2+2). It can be also viewed as the hyperbolic analog of Bogomolny equations. We uncover null forms in the nonlinearities and employ optimal bilinear estimates in the framework of wave-Sobolev spaces. As a result, we show the equation is locally wellposed in the Coulomb gauge for initial data sufficiently small in H(s) for s > 1/4
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页码：151 / 174
页数：24
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