Boundedness and large time behavior of solutions to a prey-taxis system accounting in liquid surrounding

作者：Feng, Zefu; Zhang, Mei^*

来源：NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 57: 103197.

DOI：10.1016/j.nonrwa.2020.103197

• Prey-taxis
• Boundedness
• Large time behavior

In this paper, we are concerned with the following prey-taxis system with liquid surrounding describing by the incompressible Navier-Stokes equations @@@ {n(t) + u . del n = Delta - del. (chi n del c) + gamma nF(c) - theta n - alpha n(2), x is an element of Omega, t >0, @@@ c(t) + u . del c = D Delta c - nF(c) + f(c), x is an element of Omega, t > 0, @@@ u(t) + u. del u = Delta u + del P + n del phi, del . u = 0, x is an element of Omega, t > 0, @@@ partial derivative n/partial derivative nu = partial derivative c/partial derivative nu = u = 0, x is an element of partial derivative Omega, t > 0, @@@ n(x,0) = n(0)(x), c(x,0) = c(0)(x), u(x,0) = u(0)(x), x is an element of Omega, @@@ where Omega subset of R-2 is a bounded domain with smooth boundary. Using the L-p-energy estimate, we obtain the global existence of solutions with uniform-in-time bound. Moreover, by constructing some Lyapunov functionals, we also establish the large time behavior of solutions.