Global well-posedness of the 3D non-isothermal compressible fluid model of Korteweg type. (October 2018)

• Record Type: Journal Article
• Authors: Hou, Xiaofeng; Peng, Hongyun; Zhu, Changjiang
• Is Part Of: Nonlinear analysis. Volume 43(2018)
• Page Start: 18
• Page End: 53
• Publication Date: 2018-10
• Subjects: Korteweg model -- Non-isothermal -- Global classical solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.02.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The aim of this work is to study the global existence and large-time behavior of solutions to the non-isothermal model of capillary compressible fluids derived by Dunn and Serrin (1985). It is proved that the three-dimensional non-isothermal compressible Navier–Stokes–Korteweg system admits a unique global classical solution, provided that the initial energy is suitably small. This result improves previous results obtained by Hattori and Li (1996), where the existence of global classical solutions is established for the initial data close to an equilibrium in some Sobolev space H s ( s ≥ 3 ) . Furthermore, the large time behavior of the solution is also investigated.