Global Well-posedness for the fourth order nonlinear Schrödinger equations with small rough data in high demension
نویسندگان
چکیده
For n > 2, we establish the smooth effects for the solutions of the linear fourth order Shrödinger equation in anisotropic Lebesgue spaces with k-decomposition. Using these estimates, we study the Cauchy problem for the fourth order nonlinear Schrödinger equations with three order derivatives and obtain the global well posedness for this problem with small data in modulation space M 9/2 2,1 (R ).
منابع مشابه
Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data
Abstract: For n > 3, we study the Cauchy problem for the fourth order nonlinear Schrödinger equations, for which the existence of the scattering operators and the global well-posedness of solutions with small data in Besov spaces Bs 2,1(R n) are obtained. In one spatial dimension, we get the global well-posedness result with small data in the critical homogeneous Besov spaces Ḃs 2,1. As a by-pr...
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