Well-posedness and blow-up of Virial type for some fractional inhomogeneous Choquard equations

ABSTRACT

In the subcritical energy case, local well-posedness is established in the radial energy space for a class of fractional inhomogeneous Choquard equations. The best constant of a Gagliardo–Nirenberg type inequality is obtained. Moreover, a sharp threshold of global existence versus blow-up dichotomy is obtained for mass super-critical and energy subcritical solutions.

Keywords:

• Choquard equation
• ground state
• Gagliardo–Nirenberg inequality
• virial identity
• blow-up

2010 Mathematics Subject Classification:

• 35Q55

Disclosure statement

No potential conflict of interest was reported by the author(s).