Global boundedness in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

We study the chemotaxis-Navier-Stokes system modeling coral fertilization {n(t)+u & sdot;del n=Delta n-del & sdot;(nS(x,n,c)del c)-nm, c(t)+u & sdot;del c=Delta c-c+m, m(t)+u & sdot;del m=Delta m-nm, u(t)+kappa(u & sdot;del)u+del P=Delta u+(n+m)del phi,del & sdot;u=0 in a bounded and smooth domain Omega subset of R-2, where kappa not equal 0, phi is an element of W-2,W-infinity(Omega) and S is an element of C-2(Omega<overline>x[0,infinity)2; R-2x2) fulfills |S(x,n,c)|<= S-0(c)(1+n)-alpha for all (x,n,c)is an element of Omega<overline>x[0,infinity)2 with alpha is an element of R and S-0:[0,infinity)->[0,infinity) nondecreasing. In the previous work W. Wang et al. (2021) [22], we have proved that if n|S| bears a superlinear growth of n with -1/2<alpha<0, then the corresponding initial-boundary value problem of (star) possesses a global but not necessarily bounded solution. In the present paper, we further confirm that such a global solution must be globally bounded. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.