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This paper is concerned with the two-species chemotaxis-Navier–Stokes system with Lotka–Volterra competitive kinetics
under homogeneous Neumann boundary conditions and initial conditions, where is a bounded domain in R3 with smooth boundary. Recently, in the 2-dimensional setting, global existence and stabilization of classical solutions to the above system were first established. However, the 3-dimensional case has not been studied: Because of difficulties in the Navier–Stokes system, we can...
This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function and the growth term under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that
, and
. It is shown that if is sufficiently small, then the system has a unique global-in-time classical solution that is uniformly bounded. This boundedness result is a generalization of a recent result by K. Fujie, M. Winkler, T. Yokota.
This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.
This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation
in with -initial data in the subcritical case (), where is a complex-valued unknown function, , , , , , , and . The proof is based on the - estimates of the linear semigroup and usual fixed-point argument.
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