On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations

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dc.creatorGalaktionov, V. A.
dc.creatorMitidieri, E.
dc.creatorPohozaev, S. I.
dc.date2009-02-02
dc.date.accessioned2026-07-07T12:36:58Z
dc.date.available2026-07-07T12:36:58Z
dc.descriptionThe initial boundary-value problem (IBVP) and the Cauchy problem for the Kuramoto--Sivashinsky equation and other related $2m$th-order semilinear parabolic partial differential equations in one and N dimensions are considered. Global existence and blow-up as well as uniform bounds are reviewed by using: (i) classic tools of interpolation theory and Galerkin methods, (ii) eigenfunction and nonlinear capacity methods, (iii) Henry's version of weighted Gronwall's inequalities, and (vi) two types of scaling (blow-up) arguments. For the IBVPs, existence of global solutions is proved for both Dirichlet and "Navier" boundary conditions. For some related higher-order PDEs in N dimensions uniform boundedness of global solutions of the Cauchy problem are established. As another related application, the well-posed Burnett-type equations, which are a higher-order extension of the classic Navier-Stokes equations, are studied. As a simple illustration, a generalization of the famous Leray-Prodi-Serrin-Ladyzhenskaya regularity results is obtained.
dc.description34 pages
dc.identifierhttps://arxiv.org/abs/0902.0257
dc.identifierhttp://arxiv.org/abs/0902.0257
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218277
dc.subjectAnalysis of PDEs
dc.subject35K55
dc.titleOn global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations
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