ORIGINAL ARTICLE
Well-posedness and inviscid limits for the Keller–Segel–Navier–Stokes system of the parabolic–elliptic type
Taiki Takeuchi,
Corresponding Author
Taiki Takeuchi
Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555 Japan
Correspondence
Taiki Takeuchi, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan.
Email: [email protected]
Search for more papers by this authorTaiki Takeuchi,
Corresponding Author
Taiki Takeuchi
Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555 Japan
Correspondence
Taiki Takeuchi, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan.
Email: [email protected]
Search for more papers by this authorFirst published: 20 November 2024
Abstract
We show the local well-posedness of the Keller–Segel system of the parabolic–elliptic type coupled with the Navier–Stokes system for arbitrary initial data with Sobolev regularities, where the solution is uniformly bounded with respect to the viscosity. We also show the continuous dependence of the solutions with respect to the initial data. As a result of the uniform boundedness of the solutions, we obtain inviscid limits of the system. The proof is mainly based on a priori estimates in the Sobolev spaces.
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