论文标题
对粗糙的非线性Schroedinger方程的最小质量爆破解决方案
Minimal mass blow-up solutions to rough nonlinear Schroedinger equations
论文作者
论文摘要
我们研究了聚焦的质量批评性粗糙的非线性schroedinger方程，其中随机整合以受控的粗糙路径的意义进行。如果初始数据的质量低于基态的质量，我们就会获得全球适应性。此外，在一和两个方面也获得了最小的质量爆炸溶液的存在。特别是，在随机聚焦质量批评的情况下，基态的质量正是全球拟合良好的阈值和解决方案的爆炸阈值。对于具有较低顺序扰动的一类非线性Schroedinger方程，也获得了类似的结果。
We study the focusing mass-critical rough nonlinear Schroedinger equations, where the stochastic integration is taken in the sense of controlled rough path. We obtain the global well-posedness if the mass of initial data is below that of the ground state. Moreover, the existence of minimal mass blow-up solutions is also obtained in both dimensions one and two. In particular, these yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up of solutions in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schroedinger equations with lower order perturbations.
