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 the solutions of an inhomogeneous Choquard equation

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的条件.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方程的解整体存在和爆破的条件.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.

In this paper,we mainly study the global existence and blowup conditions for the solutions of an inhomogeneous Choquard equations 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 auxiliary function.Then we get the conditions of the global existence and blowup for the solutions of the equation.Finally,according to the Cauchy-Schwartz inequality and the uncertainty principle,a new sufficient condition for the existence of blow-up of the solutions is obtained by using the mechanical analysis of a particle moving in the potential barrier field.