Global bounded solution in three-dimensional chemotaxis-Stokes model with arbitrary porous medium slow diffusion
Year: 2021
Type: preprint
Abstract: In this paper, we study the consumption-chemotaxis-Stokes model with porous medium slow diffusion in a three dimensional bounded domain with zero-flux boundary conditions and no-slip boundary condition. In recent ten years, many efforts have been made to find the global bounded solutions of chemotaxis-Stokes system in three dimensional space. Although some important progress has been carried out in some papers, as mentioned by some authors, the question of identifying an optimal condition on m ensuring global boundedness in the three-dimensional framework remains an open challenge. In the present paper, we put forward a new estimation technique, completely proved the existence of global bounded solutions for arbitrary slow diffusion case, and partially answered the open problem proposed by Winkler.
Source: arXiv (Cornell University)
Author: Jin, Chunhua
Institution: South China Normal University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1141396666, G4490756795, G6409709479
OpenAlex ID: W3123123771