Global existence for a system of Schrodinger equations with power-type nonlinearities
Journal of Mathematical Physics
American Institute of Physics
In this manuscript, we consider the Cauchy problem for a Schrödinger system with power-type nonlinearities. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Nirenberg inequality is deduced, which yields the minimal embedding constant for the inequality. Using this minimal embedding constant, global existence for small initial data is shown for the critical case p = 1 + 2/N. Finite-time blow-up, as well as stability of solutions in the critical case, is discussed.
Nguyen, N. V.; Tian, R.; Deconinck, B.; and Shiels, N., "Global existence for a system of Schrodinger equations with power-type nonlinearities" (2013). All Physics Faculty Publications. Paper 1445.