Local well-posedness for the chemotaxis-Navier-Stokes equations in Besov spaces

In this paper, we are concerned with the local well-posedness for the chemotaxis-Navier-Stokes equations in Rd, d=2,3. By fully using the advantage of weighted function generated by heat kernel and Fourier localization technique, we obtain the existence and uniqueness of smooth solutions in Besov spaces. More importantly, we show a Beale-Kato-Majda type blow-up criterion with the help of a logarithmic inequality.