论文标题
在缩放临界规则上的高度规律上的立方非线性热方程的范数通胀
Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity
论文作者
论文摘要
我们考虑了立方非线性热方程的不适性问题，并证明了Norm Efflation theHölder-Besov Space中无限丧失的规律性损失$ \ MATHCAL C^S = B^{s} _ {\ infty，\ infty，\ infty，\ infty，\ infty} $ for $ s \ le-s \ le- \ frac 23 $。特别是，我们的结果包括亚临界范围$ -1 <s \ le- \ frac 23 $，相对于Hölder -Besov量表，该范围高于缩放量表的规律$ s = -1 $。鉴于$ \ Mathcal c^s $，$ s> - \ frac 23 $的结果良好，我们的不适性结果是敏锐的。
We consider the ill-posedness issue for the cubic nonlinear heat equation and prove norm inflation with infinite loss of regularity in the Hölder-Besov space $\mathcal C^s = B^{s}_{\infty, \infty}$ for $ s \le -\frac 23$. In particular, our result includes the subcritical range $-1< s \le -\frac 23$, which is above the scaling critical regularity $s = -1$ with respect to the Hölder-Besov scale. In view of the well-posedness result in $\mathcal C^s$, $s > -\frac 23$, our ill-posedness result is sharp.
