REGULARIZING NONLINEAR SCHRODINGER EQUATIONS THROUGH PARTIAL OFF-AXIS VARIATIONS

被引:6
作者
Antonelli, Paolo [1 ]
Arbunich, Jack [2 ]
Sparber, Christof [2 ]
机构
[1] Gran Sasso Sci Inst, Laquila, Italy
[2] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
关键词
nonlinear Schrodinger equation; partial off-axis variation; Strichartz estimates; dispersion; finite-time blow-up; BBM equation; BLOW-UP;
D O I
10.1137/17M1131313
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a class of focusing nonlinear Schrodinger-type equations derived recently by Dumas, Lannes, and Szeftel within the mathematical description of high intensity laser beams. These equations incorporate the possibility of a (partial) off-axis variation of the group velocity of such laser beams through a second order partial differential operator acting in some, but not necessarily all, spatial directions. We investigate the initial value problem for such models and obtain global well-posedness in L-2-supercritical situations, even in the case of only partial off-axis dependence. This provides an answer to an open problem posed by Dumas, Lannes, and Szeftel.
引用
收藏
页码:110 / 130
页数:21
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