Braukhoff, Marcel (2017). Global (weak) solution of the chemotaxis-Navier-Stokes equations with non-homogeneous boundary conditions and logistic growth. Ann. Inst. Henri Poincare-Anal. Non Lineaire, 34 (4). S. 1013 - 1040. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1873-1430
Full text not available from this repository.Abstract
In biology, the behaviour of a bacterial suspension in an incompressible fluid drop is modelled by the chemotaxis-Navier-Stokes equations. This paper introduces an exchange of oxygen between the drop and its environment and an additionally logistic growth of the bacteria population. A prototype system is given by {n(t) + u . del(n) = Delta n - (n del c) + n - n(2), x is an element of Omega, t > 0, c(t) + u . del c = Delta c - nc, x is an element of Omega, t > 0, u(t) = Delta(u) + u . del 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 in conjunction with the initial data (n, c, u)(., 0) = (n(0), c(0), u(0)) and the boundary conditions partial derivative c/partial derivative nu = 1 -c, partial derivative n/partial derivative nu = n partial derivative c/partial derivative nu, u = 0, x is an element of partial derivative Omega, t > 0. Here, the fluid drop is described by Omega subset of R-N being a bounded convex domain with smooth boundary. Moreover, phi is a given smooth gravitational potential. Requiring sufficiently smooth initial data, the existence of a unique global classical solution for N = 2 is proved, where parallel to n parallel to L-p(Omega) is bounded in time for all p < infinity, as well as the existence of a global weak solution for N = 3. (C) 2016 Elsevier Masson SAS. All rights reserved. .
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-226187 | ||||||||
| DOI: | 10.1016/j.anihpc.2016.08.003 | ||||||||
| Journal or Publication Title: | Ann. Inst. Henri Poincare-Anal. Non Lineaire | ||||||||
| Volume: | 34 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | S. 1013 - 1040 | ||||||||
| Date: | 2017 | ||||||||
| Publisher: | ELSEVIER SCIENCE BV | ||||||||
| Place of Publication: | AMSTERDAM | ||||||||
| ISSN: | 1873-1430 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/22618 |
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