The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:476

Article

Fonseca, German¹  Pastran, Ricardo¹  Rodriguez-Blanco, Guillermo¹ 

[1] Univ Nacl Colombia, AK 30 45-03, Bogota, Colombia

关键词: Benjamin-Ono equation;    Local and global well-posedness;    Sobolev spaces;    Weighted Sobolev spaces;   

DOI  :  10.1016/j.jmaa.2019.03.047

来源: Elsevier

【 摘 要 】

We prove that the initial value problem associated to a nonlocal perturbation of the Benjamin-Ono equation is locally and globally well-posed in Sobolev spaces H-s(R) for any s > -3/2 and we establish that our result is sharp in the sense that the flow map of this equation fails to be C-2 in H-s(R) for s < -3/2. Finally, we study persistence properties of the solution flow in the weighted Sobolev spaces Z(s,r) = H-s(R) boolean AND L-2 (vertical bar x vertical bar(2r) dx) for s >= r > 0. We also prove some unique continuation properties of the solution flow in these spaces. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free