带有幂型的广义Zakharov方程组解的爆破率的下界估计

主要研究了关于R~2中一类带有幂型非线性的广义Zakharov方程组的Cauchy问题的有限时间爆破解的爆破率的下界估计.在α≤0和p≥3条件下,对于Cauchy问题任意给定的属于能量空间H~1(R~2)×L~2(R~2)×L~2(R~2)的有限时间的爆破解,得到了对于t靠近有限爆破时间T时的爆破率的最优下界估计.此外,给出了Cauchy问题维里等式的一个应用.

Lower-Bound Estimates for the Blow-up Rate of Solutions to the Generalized Zakharov Equations with a Power-Type Nonlinearity

This paper is concerned with lower-bound estimates for the blow-up rate of a finite-time blow-up solution to the Cauchy problem for a class of generalized Zakharov equations with a power-type nonlinearity in $\mathbb{R}^2$. Under the conditions $\alpha\leq 0$ and $p\geq 3$, for a given finite-time blow-up solution to the Cauchy problem in the energy space $H^{1}({\mathbb{R}}^{2})\times L^{2}({\mathbb{R}}^{2})\times L^{2}({\mathbb{R}}^{2})$, the authors obtain optimal lower-bound estimates for the blow-up rate of the finite-time blow-up solution for $t$ near the finite blow-up time $T$. In addition, an application of the Virial identity of the Cauchy problem is given.