Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation

2019/11/11 by Seong, Kihoon
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.04041

Abstract

We consider the low regularity behavior of the fourth order cubic nonlinear Schrödinger equation (4NLS) \begincases i∂_tu+∂_x⁴u=± \vert u \vert²u, (t,x)∈ ℝ× ℝ
u(x,0)=u₀(x)∈ H^s(ℝ). \endcases In arXiv:1911.03253, the author showed that this equation is globally well-posed in H^s, s≥ -(1)/(2) and ill-posedness in the sense that the solution map fails to be uniformly continuous for -(15)/(14)

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