Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data
We study the initial value problem for the 3-D Euler equation when the fluid is inviscid and incompressible, and flows with axisymmetry and without swirl. On the initial vorticity $omega_0$, we assumed that $omega_0/r$ belongs to $L(log L (Bbb R^3))^{alpha}$ with $alpha >1/2$, where $r$ is the di...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
1998-10-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1998/26/abstr.html |
| _version_ | 1818556406303817728 |
|---|---|
| author | Dongho Chae Oleg Yu Imanuvilov |
| author_facet | Dongho Chae Oleg Yu Imanuvilov |
| author_sort | Dongho Chae |
| collection | DOAJ |
| description | We study the initial value problem for the 3-D Euler equation when the fluid is inviscid and incompressible, and flows with axisymmetry and without swirl. On the initial vorticity $omega_0$, we assumed that $omega_0/r$ belongs to $L(log L (Bbb R^3))^{alpha}$ with $alpha >1/2$, where $r$ is the distance to an axis of symmetry. To prove the existence of weak global solutions, we prove first a new a priori estimate for the solution. |
| first_indexed | 2024-12-13T23:46:56Z |
| format | Article |
| id | doaj.art-200ae6e7d6a44ace9b7e72119c81c9ab |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T23:46:56Z |
| publishDate | 1998-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-200ae6e7d6a44ace9b7e72119c81c9ab2022-12-21T23:26:55ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911998-10-01199826117Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial dataDongho ChaeOleg Yu ImanuvilovWe study the initial value problem for the 3-D Euler equation when the fluid is inviscid and incompressible, and flows with axisymmetry and without swirl. On the initial vorticity $omega_0$, we assumed that $omega_0/r$ belongs to $L(log L (Bbb R^3))^{alpha}$ with $alpha >1/2$, where $r$ is the distance to an axis of symmetry. To prove the existence of weak global solutions, we prove first a new a priori estimate for the solution.http://ejde.math.txstate.edu/Volumes/1998/26/abstr.htmlEuler equationsaxisymmetryweak solution. |
| spellingShingle | Dongho Chae Oleg Yu Imanuvilov Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data Electronic Journal of Differential Equations Euler equations axisymmetry weak solution. |
| title | Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data |
| title_full | Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data |
| title_fullStr | Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data |
| title_full_unstemmed | Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data |
| title_short | Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data |
| title_sort | existence of axisymmetric weak solutions of the 3 d euler equations for near vortex sheet initial data |
| topic | Euler equations axisymmetry weak solution. |
| url | http://ejde.math.txstate.edu/Volumes/1998/26/abstr.html |
| work_keys_str_mv | AT donghochae existenceofaxisymmetricweaksolutionsofthe3deulerequationsfornearvortexsheetinitialdata AT olegyuimanuvilov existenceofaxisymmetricweaksolutionsofthe3deulerequationsfornearvortexsheetinitialdata |