We consider the half-wave equation $i{u}_t=Du-|u{|}^{\frac{2}{3}}u$ in three dimensions and in the mass critical. For initial data $u(t_0,x)=u_0(x)\in H_{rad}^{1/2+\delta }({\mathbb{R}}^3)$ with radial symmetry, we construct a new class of the radial blowup solutions with the blow up rate ${\Vert D^{\frac{1}{2}}u(t)\Vert }_2\sim \frac{C(u_0)}{|t|}$ as $t\to 0^{-}$.

中文翻译：

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3D 质量临界半波方程的爆破动力学

我们考虑半波方程 $\mathrm{一世}{你}_{吨}=D你-|你{|}^{\frac{2}{3}}你$在三个维度和质量临界。对于初始数据$你({吨}_0,X)={你}_0(X)\in H_{r\mathrm{一种}d}^{1/2+\delta }({\mathbb{电阻}}^3)$ 使用径向对称，我们构造了一类新的径向膨胀解，其膨胀率 ${\Vert D^{\frac{1}{2}}你(吨)\Vert }_2～\frac{C({你}_0)}{|吨|}$ 作为 $吨\to 0^{-}$.