Work

Well‐posedness and inviscid limits for the Keller–Segel–Navier–Stokes system of the parabolic–elliptic type

Year: 2024

Type: article

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.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.202300304

Author: Taiki Takeuchi

Institution: Waseda University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Japan Society for the Promotion of Science, Japan Science and Technology Agency

Awards: Solvability and regularity of solutions for the chemotaxis system by the method of functional analysis, G1699881565, Maximal regularity theory of the Fujita-type equation based on the harmonic analysis