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...
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Published in | arXiv.org |
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Main Authors | , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
18.10.2020
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 2331-8422 |