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

Author(s)

Carvajal, Xavier ^[1] ; Panthee, Mahendra ^[2]

Affiliation

^[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

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 417, n. 1, p. 1-22, SEP 1 2014.
• Web of Science Citations: 1

Abstract

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. (AU)

• FAPESP's process: 12/20966-4 - Well-posedness of the Cauchy problem and stability theory for nonlinear dispersive equations
• Grantee: Mahendra Prasad Panthee
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/23054-6 - Properties of solutions of some dispersive equations
• Grantee: Marcia Assumpcao Guimaraes Scialom
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil