Global existence for a coupled system of Schrödinger equations with power-type nonlinearities
نویسندگان
چکیده
u j : RN ×R → C, ψ j0 : RN → C for j = 1, 2, . . . , m and ajk = akj are positive real numbers. 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. C © 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4774149]
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