The Cauchy problem for dissipative Benjamin-Ono equation in weighted Sobolev spaces

被引：5

作者：

Cunha, Alysson ^{[1
]}

机构：

[1] Univ Fed Goias UFG, IME, BR-74001970 Goiania, Go, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 492卷 / 02期

关键词：

Well-posedness; dBO equation; Weighted Sobolev spaces; Fourier transform; Stein derivative; Unique continuation principles; ZAKHAROV-KUZNETSOV EQUATION; GLOBAL WELL-POSEDNESS; BURGERS EQUATION; INVISCID LIMIT; IVP; VERSION; WAVES;

D O I：

10.1016/j.jmaa.2020.124468

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the well-posedness in weighted Sobolev spaces, for the initial value problem (IVP) associated with the dissipative Benjamin-Ono (dBO) equation. We establish 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), s >= r > 0. We also prove some unique continuation properties in these spaces. In particular, such results of unique continuation show that our results of well posedness are sharp. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：28

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