论文标题
II型三维能量临界热方程的有限时间爆破
Type II Finite time blow-up for the three dimensional energy critical heat equation
论文作者
论文摘要
我们考虑三维能量关键热量方程\ begin {equation*} \ begin {case} u_t =ΔU+u^{5}，〜＆\ mbox {in} {\ Mathbb r}^3。 \ end {cases} \ end {equation*} 我们构建II型有限时间爆破解决方案$ u（x，t）$，并使用爆炸率$ \ | u \ | _ {l^\ infty} \ sim（t-t）^{ - k} $，其中$ k = 1,2，... $。这给出了Filippas，Herrero和Velazquez \ Cite {FHV}的正式计算的严格证明。这是三维能量临界热方程的II型有限时间爆破的第一个实例。
We consider the following Cauchy problem for three dimensional energy critical heat equation \begin{equation*} \begin{cases} u_t=Δu+u^{5},~&\mbox{ in } \ {\mathbb R}^3 \times (0,T),\\ u(x,0)=u_0(x),~&\mbox{ in } \ {\mathbb R}^3. \end{cases} \end{equation*} We construct type II finite time blow-up solution $u(x,t)$ with the blow-up rates $ \| u\|_{L^\infty} \sim (T-t)^{-k}$, where $ k=1,2,... $. This gives a rigorous proof of the formal computations by Filippas, Herrero and Velazquez \cite{fhv}. This is the first instance of type II finite time blow-up for three dimensional energy critical heat equation.
