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Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid
| Content Provider | Semantic Scholar |
|---|---|
| Author | Desjardins, Benoît Esteban, Maria J. |
| Copyright Year | 1999 |
| Abstract | Abstract. We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of $\R^d$ $(d=2$ or $3)$ with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence of solutions for initial velocities in $H^1_0(\Omega)$. In the absence of collisions, solutions exist for all time in dimension 2, whereas in dimension 3 the lifespan of solutions is infinite only for small enough data. |
| Starting Page | 59 |
| Ending Page | 71 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s002050050136 |
| Volume Number | 146 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s002050050136 |
| Alternate Webpage(s) | https://doi.org/10.1007/s002050050136 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
