Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
A class of semiflows having possibly nonunique solutions is defined. The measurability and continuity properties of such generalized semiflows are studied. It is shown that a generalized semiflow has a global attractor if and only if it is pointwise dissipative and asymptotically compact. The struct...
| Auteur principal: | |
|---|---|
| Format: | Journal article |
| Publié: |
1997
|
| _version_ | 1826298374229327872 |
|---|---|
| author | Ball, J |
| author_facet | Ball, J |
| author_sort | Ball, J |
| collection | OXFORD |
| description | A class of semiflows having possibly nonunique solutions is defined. The measurability and continuity properties of such generalized semiflows are studied. It is shown that a generalized semiflow has a global attractor if and only if it is pointwise dissipative and asymptotically compact. The structure of the global attractor in the presence of a Lyapunov function, and its connectedness and stability properties are studied. In particular, examples are given in which the global attractor is a single point but is not Lyapunov stable. The existence of a global attractor for the 3D incompressible Navier-Stokes equations is established under the (unproved) hypothesis that all weak solutions are continuous from (0, ∞) to L2. |
| first_indexed | 2024-03-07T04:45:51Z |
| format | Journal article |
| id | oxford-uuid:d33de03c-e743-4ace-a024-1b2bbcba1b89 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:45:51Z |
| publishDate | 1997 |
| record_format | dspace |
| spelling | oxford-uuid:d33de03c-e743-4ace-a024-1b2bbcba1b892022-03-27T08:09:51ZContinuity properties and global attractors of generalized semiflows and the Navier-Stokes equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d33de03c-e743-4ace-a024-1b2bbcba1b89Symplectic Elements at Oxford1997Ball, JA class of semiflows having possibly nonunique solutions is defined. The measurability and continuity properties of such generalized semiflows are studied. It is shown that a generalized semiflow has a global attractor if and only if it is pointwise dissipative and asymptotically compact. The structure of the global attractor in the presence of a Lyapunov function, and its connectedness and stability properties are studied. In particular, examples are given in which the global attractor is a single point but is not Lyapunov stable. The existence of a global attractor for the 3D incompressible Navier-Stokes equations is established under the (unproved) hypothesis that all weak solutions are continuous from (0, ∞) to L2. |
| spellingShingle | Ball, J Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations |
| title | Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations |
| title_full | Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations |
| title_fullStr | Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations |
| title_full_unstemmed | Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations |
| title_short | Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations |
| title_sort | continuity properties and global attractors of generalized semiflows and the navier stokes equations |
| work_keys_str_mv | AT ballj continuitypropertiesandglobalattractorsofgeneralizedsemiflowsandthenavierstokesequations |