一类非齐次Choquard方程的解整体存在与爆破的条件

Global existence and blowup conditions for 调和solutions of an inhomogeneous Choquard equation

摘要:

本文研究了一类非齐次Choquard方程在初值质能高于其基态质能情形下的解的整体存在与爆破条件. 本文利用Gagliardo-Nirenberg不等式及Virial恒等式构造了一个辅助函数，并由该函数的凸性获得了初值质能高于基态质能的等价刻画，进而得到了Choquard方程的解整体存在与爆破的条件. 此外，本文还根据Cauchy-Schwartz不等式和不确定原理，借助一个粒子在具有势垒场中运动的力学分析，得到了一个新的解爆破存在的充分条件.

Abstract:

In this paper, we mainly study the global existence and blowup conditions for the solutions of an inhomogeneous Choquard equation when the initial data is above the ground state"s mass-energy. Firstly, an auxiliary function is constructed by the Gagliardo-Nirenberg inequality and Virial identity, while an equivalent characterization of the initial data above the ground state"s mass-energy is obtained by using the convexity of the function. Then we get the conditions of the global existence and blowup for the Choquard equation. Finally, according to the Cauchy-Schwartz inequality and the uncertainty principle, a new sufficient condition for the existence of blow-up solutions is obtained by using the mechanical analysis of a particle moving in potential barrier field.