Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 62, Issue 4, Pages -Publisher
AIP Publishing
DOI: 10.1063/5.0029161
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Funding
- National Natural Science Foundation of China [11601053, 11526042]
- Natural Science Foundation of Chongqing [cstc2019jcyj-msxmX0082]
- South Africa-China Young Scientist Exchange Programme, 2020
- European Mathematical Society
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This paper discusses an attraction-repulsion Navier-Stokes system with signal-dependent motility and sensitivity in a two-dimensional smooth bounded domain, modeling cells' reaction to two chemical signals in a liquid environment and density-suppressed motility during stripe pattern formation. Through a new weighted energy method, it is proven that under certain assumptions, the system has a unique global classical solution that is uniformly bounded in time, and the global solution exponentially converges to a constant steady state.
This paper is concerned with an attraction-repulsion Navier-Stokes system with signal-dependent motility and sensitivity in a two-dimensional smooth bounded domain under zero Neumann boundary conditions for n, c, v and the homogeneous Dirichlet boundary condition for u. This system describes the evolution of cells that react on two different chemical signals in a liquid surrounding environment and models a density-suppressed motility in the process of stripe pattern formation through the self-trapping mechanism. The major difficulty in analysis comes from the possible degeneracy of diffusion as c and v tend to infinite. Based on a new weighted energy method, it is proved that under appropriate assumptions on parameter functions, this system possesses a unique global classical solution, which is uniformly-in-time bounded. Moreover, by means of energy functionals, it is shown that the global bounded solution of the system exponentially converges to the constant steady state.
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