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Global existence of free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass. (English) Zbl 1514.35442

Summary: We consider a coupled Patlak-Keller-Segel-Navier-Stokes system in \(\mathbb{R}^2\) that describes the collective motion of cells and fluid flow, where the cells are attracted by a chemical substance and transported by ambient fluid velocity, and the fluid flow is forced by the friction induced by the cells. The main result of the paper is to show the global existence of free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35Q35 PDEs in connection with fluid mechanics
76Z05 Physiological flows
92C17 Cell movement (chemotaxis, etc.)
92C35 Physiological flow
35B65 Smoothness and regularity of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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