论文标题
关于双功率非线性schrödinger方程的最小质量吹式质量吹式解决方案的评论
Remarks on minimal mass blow up solutions for a double power nonlinear Schrödinger equation
论文作者
论文摘要
我们考虑具有双重功率非线性的以下非线性schrödinger方程\ [i \ frac {\ partial u} {\ partial t}+ΔU+| u | $ \ mathbb {r}^n $。对于$ n = 1,2,3 $，Le Coz-Martel-Raphaël（2016）构建了一种最小的质量爆破解决方案。此外，先前的研究得出了爆炸解决方案的爆炸率。在本文中，我们将此结果扩展到一般维度。此外，我们研究了爆炸时间附近的临界质量爆破解决方案的行为。
We consider the following nonlinear Schrödinger equation with double power nonlinearity \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u+|u|^{p-1}u=0,\quad 1<p<1+\frac{4}{N} \] in $\mathbb{R}^N$. For $N=1,2,3$, Le Coz-Martel-Raphaël (2016) construct a minimal-mass blow-up solution. Moreover, the previous study derives blow-up rate of the blow-up solution. In this paper, we extend this result to the general dimension. Furthermore, we investigate the behaviour of the critical mass blow-up solution near the blow-up time.
