Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes system. (English) Zbl 1475.35002
Summary: This paper proves some uniqueness results of weak solutions to a Keller-Segel-Navier-Stokes system in a bounded domain \(\Omega \subset \mathbb{R}^N\) (\(N \geq 3\)) under some conditions. As a by-product, we show that these conditions hold true when \(N = 2\) for the Keller-Segel-Navier-Stokes system with a logistic term.
MSC:
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K59 | Quasilinear parabolic equations |
| 35Q30 | Navier-Stokes equations |
| 92C17 | Cell movement (chemotaxis, etc.) |
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