一类带幂型非线性薛定谔方程组的爆破准则

On blow-up criterion for a class of Schrödinger system with power-type nonlinearities

研究了一类带幂型非线性薛定谔方程组解的爆破问题。通过应用局部维里等式和几乎有限传播速度,证明了当空间维数n≥3且能量E(u_(0),v_(0))<0时,方程组的解(u,v)发生有限时刻或无穷时刻爆破。

The blow-up of the solution to a class of Schrödinger system with power-type nonlinearities is studied.By the local Virial identities and almost finite velocity of propagation,the solution(u,v)to the system blows up at finite time or infinite time under the assumptions that the space dimension n≥3and the energy E(u_(0),v_(0))<0.