Well-posedness for a higher-order Benjamin-Ono equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Linares, Felipe¹  Pilod, Didier²  Ponce, Gustavo³ 

[1] IMPA, BR-22460320 Rio De Janeiro, Brazil

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

关键词: Benjamin-Ono equation;    Local well posedness;    Gauge transformation;   

DOI  :  10.1016/j.jde.2010.08.022

来源: Elsevier

【 摘 要 】

In this paper we prove that the initial value problem associated to the following higher-order Benjamin-Ono equation partial derivative(t)v - bH partial derivative(2)(x)v + a partial derivative(3)(x)v = cv partial derivative(x)v - d partial derivative(x)(vH partial derivative(x)v + H(v partial derivative(x)v)) where x t is an element of R v is a real-valued function H is the Hilbert transform a is an element of R b c and d are positive constants is locally well-posed for initial data v(0) = v(0) is an element of H-5(R) s >= 2 or v(0) is an element of H-k(R) boolean AND L-2(R x(2) dx) k is an element of Z(+) k >= 2 (C) 2010 Elsevier Inc All rights reserved

【 授权许可】

Free