论文标题
3D中质量关键半波方程的爆炸动力学
Blowup dynamics for Mass Critical Half-wave equation in 3D
论文作者
论文摘要
我们考虑半波方程$ i u_t = du- | u |^{\ frac {2} {3}} u $在三个维度和质量批评中。对于初始数据，$ u（t_0，x）= u_0（x）\ in H^{1/2} _ {rad}（\ Mathbb {r}^3）$ fith radial Symmetry，我们构建了新的最小质量爆炸解决方案，并使用爆破率$ \ | d^{\ frac {1} {2}} u（t）\ | _2 \ sim \ frac {c（u_0）} {| t |^|^{\ frac {1} {1} {4}}}}}} $ as T \ rightArrow0^ - $。
We consider the half-wave equation $i u_t=Du-|u|^{\frac{2}{3}}u$ in three dimension and in the mass critical. For initial data $u(t_0,x)=u_0(x)\in H^{1/2}_{rad}(\mathbb{R}^3)$ with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate $\|D^{\frac{1}{2}}u(t)\|_2\sim\frac{C(u_0)}{|t|^{\frac{1}{4}}}$ as $t\rightarrow0^-$.
