Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 73, Issue 3, Pages -Publisher
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-022-01752-6
Keywords
Chemotaxis; Fluid; Logistic source; Generalized solution
Categories
Funding
- National Natural Science Foundation of China [11671021, 11671066, 12101377]
- National Nature Science Foundation of China [12101377]
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This paper studies the global solvability of a two-dimensional chemotaxis-fluid model, and shows that persistent Dirac-type singularities can be ruled out without imposing any critical superlinear exponent restriction on the logistic source function.
In this paper, we study a chemotaxis-fluid model in a two-dimensional setting as below, {n(t) + u . del n = Delta n - del . (n del c) + f(n), x is an element of Omega, t > 0, c(t) + u .del c = Delta c - c + n, x is an element of Omega, t > 0, u(t) = Delta u + del P + n del phi, x is an element of Omega, t > 0, del . u = 0, x is an element of Omega, t > 0. The global solvability of the system in a generalized sense is obtained under the hypothesis that the logistic source function f is an element of C-1 ([0, infinity)) as satisfies a very mild condition: f (0) >= 0 and f(s)/s -> -infinity as s -> infinity. This result exhibits that without any critical superlinear exponent restriction on f, persistent Dirac-type singularities can be ruled out in our model. This work can be regarded as a natural follow-up to the recent paper due to Winkler.
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