Global Well-posedness for The Fourth-order Nonlinear Schrödinger Equations on ℝ²

2023/08/11 by Başakoğlu, Engin, Yeşiloğlu, Barış, Yılmaz, Oğuz
#35A01 #35A02 #35G25 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.06210

Abstract

We study the global well-posedness of the two-dimensional defocusing fourth-order Schrödinger initial value problem with power type nonlinearities \vert u\vert^2ku where k is a positive integer. By using the I-method, we prove that global well-posedness is satisfied in the Sobolev spaces H^s(ℝ²) for 2-(3)/(4k)

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