The unique global solvability of the nonhomogeneous incompressible asymmetric fluids with vacuum

The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension \(d= 2,3\). The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and \(H^{1}\) initial velocities. We first construct the global existence...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Xu, Fuyi, Zhang, Mingxue, Qiao, Liening
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.10.2020
Subjects
Asymmetry
Fluid dynamics
Fluid flow
Incompressible flow
Uniqueness
Online AccessGet full text

Cover

More Information
Summary:The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension \(d= 2,3\). The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and \(H^{1}\) initial velocities. We first construct the global existence of the solution with large data in 2-D. Next, we establish the existence of local in time solution for arbitrary large data and global in time for some smallness conditions in 3-D. Finally, the uniqueness of the solution is proved under quite soft assumptions about its regularity through a Lagrangian approach. In particular, the initial vacuum is allowed.
ISSN:2331-8422