4.5 Article

GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR THE 3D AXISYMMETRIC CHEMOTAXIS-NAVIER-STOKES EQUATIONS WITH NONLINEAR DIFFUSION

Journal

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 42, Issue 9, Pages 4489-4522

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2022062

Keywords

Global existence; weak solutions; chemotaxis; Navier-Stokes

Funding

  1. Postgraduate Innovation Foundation of Hebei University [HBU2022ss013]
  2. Natural Science Foundation of Hebei Province [A2020201014, A2019201106]
  3. Second Batch of Young Talents of Hebei Province
  4. Nonlinear Analysis Innovation Team of Hebei University

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This paper considers the Cauchy problem for the three-dimensional axisymmetric chemotaxis-Navier-Stokes equations with nonlinear diffusion Delta n(m). By utilizing the structure of axisymmetric flow without swirl, the author shows the global existence of weak solutions for the chemotaxis-Navier-Stokes equations with m = 5/3.
In this paper, we consider the Cauchy problem for the three dimensional axisymmetric chemotaxis-Navier-Stokes equations with nonlinear diffusion Delta n(m). Taking advantage of the structure of axisymmetric flow without swirl, we show the global existence of weak solutions for the chemotaxis-Navier-Stokes equations with m = 5/3.

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