Global well-posedness for the radial defocusing cubic wave equation on $R^3$ and for rough data

Electronic Journal of Differential Equations

关键词: Nonlinear Schrodinger equation;    well-posedness;   

DOI  :  

来源: DOAJ

【 摘 要 】

We prove global well-posedness for the radial defocusing cubicwave equation$$displaylines{partial_{tt} u- Delta u=-u^{3} cru(0,x) =u_{0}(x)crpartial_{t} u(0,x)=u_{1}(x)}$$with data $(u_0, u_1) in H^{s} imes H^{s-1}$,$1 > s >7/10$. The proof relies upon a Morawetz-Strauss-typeinequality that allows us to control the growth of an almostconserved quantity.

【 授权许可】

Unknown