带斯塔克势的非线性Schrdinger方程L^2集中性质

L^2-concentration Properties for Nonlinear Schrdinger Equation with Stark Potential

讨论了带斯塔克势的非线性Schrd inger方程爆破解的定性性质,运用一个变量替换建立了带斯塔克势的非线性Schrd inger方程与不带势的经典非线性Schrd inger方程之间的联系.结合经典非线性Schrd inger方程的性质,进一步研究了临界的带斯塔克势的非线性Schrd inger方程爆破解的结构,证明了其爆破解具有L2集中性质.特别地,当初始值条件径向对称时,证明了原点O为集中点.

We study the qualitative property of critical nonlinear Schroedinger equation with Stark potential, using a transformation of variables, we establish the relation between the nonlinear Schroedinger equations with and without Stark potential. Combined with the properties of the nonlinear Schroedinger equation without potential, we study the structure of the blow-up solutions of the critical Schoedinger equation with a Stark potential, we prove that the blow-up solutions have center L^2-concentration property. Especially, if the initial data is radially symmetric, the origin is the concentration point.