Artículos de revistas
On the well-posedness of higher order viscous Burgers' equations
Registro en:
Journal Of Mathematical Analysis And Applications. Academic Press Inc Elsevier Science, v. 417, n. 1, n. 1, n. 22, 2014.
0022-247X
1096-0813
WOS:000335488900001
10.1016/j.jmaa.2014.02.056
Autor
Carvajal, X
Panthee, M
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 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. 417 1 1 22 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) FAEPEX [1486/12] Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) FAPESP [2012/23054-6, 2012/20966-4] FAEPEX [1486/12] CNPq [479558/2013-2]