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

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.

Key words:Choquard equation; Global existence; Blow-up; Virial identity