The global wellposedness of the 3D heat-conducting viscous incompressible fluids with bounded density. (April 2015)

• Record Type: Journal Article
• Authors: Zhang, Xu; Tan, Zhong
• Is Part Of: Nonlinear analysis. Volume 22(2015)
• Page Start: 129
• Page End: 147
• Publication Date: 2015-04
• Subjects: Inhomogeneous incompressible fluids -- Optimal decay rates -- Energy method -- Sobolev interpolation -- Heat conducting; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.08.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the global wellposedness of the inhomogeneous incompressible heat-conducting viscous fluids in three dimension space. We generalize the result of Fujita & Kato for Navier–Stokes to the heat-conducting inhomogeneous incompressible viscous fluids. The key point is that we get the global wellposedness under the assumption that the initial density has positive lower and upper bound and the initial temperature can be arbitrarily large.