Global existence and boundedness of classical solutions in chemotaxis-(Navier-)Stokes system with singular sensitivity and self-consistent term

This paper addresses the global existence and boundedness of classical solutions to the Neumann-Neumann-Dirichlet value problem for the chemotaxis system, as described by {+.del=-del.(/1+del)+del.(del), is an element of , > 0, + .del = -, is an element of , > 0, + del = - del + /1+del , is an element of , > 0, del.=0, is an element of , > 0 / = / = 0, = 0, is an element of , > 0 (, 0) = (0)(), (, 0) = (0)(), (, 0) = (0)(), is an element of in a smoothly bounded domain subset of R ( = 2, 3), where >0 and the gravitational potential function Phi is an element of W-1,W-infinity(Omega). It is confirmed that for any selection of chi satisfying 0 < <= root(22)1ln2(1+||(0)||(infinity()))+(-1)(2)((2)+ln(2)(1+||(0)||(infinity())))-1ln(1+||(0)||(infinity()))/(-1)ln(1+||(0)||(infinity())) with ->/2 and (1) -> - 1, then the corresponding problem (*) admits a globally and uniformly bounded classical solution via an approach to introduce a trigonometric-type weight function.