On the well-posedness of higher order viscous Burgers' equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:417

Article

Carvajal, Xavier¹  Panthee, Mahendra² 

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941972 Rio de Janeiro, RJ, Brazil

[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP, Brazil

关键词: Initial value problem;    Well-posedness;    KdV equation;    Dispersive-dissipative models;   

DOI  :  10.1016/j.jmaa.2014.02.056

来源: Elsevier

【 摘 要 】

We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the L-2-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle argument to prove local well-posedness for data with Sobolev regularity below L-2. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation p, and nonlinearity k + 1, satisfy a relation p = 2k + 1. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free