SCATTERING FOR DEFOCUSING ENERGY SUBCRITICAL NONLINEAR WAVE EQUATIONS

被引:8
作者
Dodson, Benjamin [1 ]
Lawrie, Andrew [2 ]
Mendelson, Dana [3 ]
Murphy, Jason [4 ]
机构
[1] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA
[2] MIT, Dept Math, Cambridge, MA 02139 USA
[3] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[4] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA
关键词
nonlinear waves; scattering; GLOBAL WELL-POSEDNESS; BLOW-UP RATE; SCHRODINGER-EQUATION; RADIAL SOLUTIONS; DIMENSIONS; REGULARITY; NLS;
D O I
10.2140/apde.2020.13.1995
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the Cauchy problem for the defocusing power-type nonlinear wave equation in (1+3)-dimensions for energy subcritical powers p in the superconformal range 3 < p < 5. We prove that any solution is global-in-time and scatters to free waves in both time directions as long as its critical Sobolev norm stays bounded on the maximal interval of existence.
引用
收藏
页码:1995 / 2090
页数:96
相关论文
共 55 条
[1]   High frequency approximation of solutions to critical nonlinear wave equations [J].
Bahouri, H ;
Gérard, P .
AMERICAN JOURNAL OF MATHEMATICS, 1999, 121 (01) :131-175
[2]   Decay estimates for the critical semilinear wave equation [J].
Bahouri, H .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1998, 15 (06) :783-789
[3]  
Bahouri H, 2006, INT MATH RES NOTICES, V2006
[4]   Self-similar solutions of the cubic wave equation [J].
Bizon, P. ;
Breitenlohner, P. ;
Maison, D. ;
Wasserman, A. .
NONLINEARITY, 2010, 23 (02) :225-236
[5]  
BULUT A, 2012, RECENT ADV HARMONIC, V0581, P00001
[6]   Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation [J].
Bulut, Aynur .
JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (06) :1609-1660
[7]   CHARACTERIZATION OF LARGE ENERGY SOLUTIONS OF THE EQUIVARIANT WAVE MAP PROBLEM: I [J].
Cote, R. ;
Kenig, C. E. ;
Lawrie, A. ;
Schlag, W. .
AMERICAN JOURNAL OF MATHEMATICS, 2015, 137 (01) :139-207
[8]  
Dodson B., 2018, GLOBAL WELL POSEDNES
[9]   Global well-posedness and scattering for the radial, defocusing, cubic wave equation with almost sharp initial data [J].
Dodson, Benjamin .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2018, 43 (10) :1413-1455
[10]   GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE RADIAL, DEFOCUSING, CUBIC WAVE EQUATION WITH INITIAL DATA IN A CRITICAL BESOV SPACE [J].
Dodson, Benjamin .
ANALYSIS & PDE, 2019, 12 (04) :1023-1048