Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrodinger equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:296

Article

Liu, Xuan¹  Zhang, Ting¹ 

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China

关键词: Schrodinger equation;    Bilinear Strichartz's estimate;    Local well-posedness;    Besov spaces;   

DOI  :  10.1016/j.jde.2021.06.007

来源: Elsevier

【 摘 要 】

In this paper, we consider the well-posedness of the inhomogeneous nonlinear biharmonic Schrodinger equation with spatial inhomogeneity coefficient K(x) behaves like vertical bar x vertical bar(-b) for 0 < b < min {N/2, 4}. We show the local well-posedness in the whole H-s-subcritical case, with 0 < s <= 2. The difficulties of this problem come from the singularity of K(x) and the lack of differentiability of the nonlinear term. To resolve this, we derive the bilinear Strichartz's type estimates for the nonlinear biharmonic Schrodinger equations in Besov spaces. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free