×

A note on global existence for the chemotaxis-Stokes model with nonlinear diffusion. (English) Zbl 1323.35184

Summary: This note is concerned with the Cauchy problem on the 3D chemotaxis-Stokes equations with nonlinear diffusions and large initial data. We prove the global existence of weak solutions for all adiabatic exponents \(m\in[1,+\infty)\). In particular, the result fills up the gap between \(m=1\) by M. Winkler [Commun. Partial Differ. Equations 37, No. 1–3, 319–351 (2012; Zbl 1236.35192)] and \(m\in(\frac{4}{3},2]\) by J.-G. Liu and A. Lorz [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 5, 643–652 (2011; Zbl 1236.92013)]. A similar result also holds for the 2D chemotaxis-Navier-Stokes equations.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C17 Cell movement (chemotaxis, etc.)
PDFBibTeX XMLCite
Full Text: DOI