相关论文: Large time behavior of solutions to the $3$D aniso…
We consider the large time behavior of the solution to the anisotropic Navier--Stokes equations in a $3$D half-space. Investigating the precise anisotropic nature of linearized solutions, we obtain the optimal decay estimates for the…
In this paper, we study the decay rates for the global small smooth solutions to 3D anisotropic incompressible Navier-Stokes equations. In particular, we prove that the horizontal components of the velocity field decay like the solutions of…
In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.
The asymptotic behavior of weak time-periodic solutions to the Navier-Stokes equations with a drift term in the three-dimensional whole space is investigated. The velocity field is decomposed into a time-independent and a remaining part,…
In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the…
We use the vorticity formulation to study the long-time behavior of solutions to the Navier-Stokes equation on R^3. We assume that the initial vorticity is small and decays algebraically at infinity. After introducing self-similar…
We consider three dimensional incompressible Navier-Stokes equation $(NS)$ with different viscous coefficient in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared to the…
We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conductive gases in $\mathbb{R}^3$. More precisely, under a suitable additional condition involving only the low frequencies of…
We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the…
In this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near…
The stability problem for the 2D Navier-Stokes equations with dissipation in only one direction on $\mathbb R^2$ is not fully understood. This dissipation is in the intermediate regime between the fully dissipative Navier-Stokes and the…
The nonhomogeneous Navier-Stokes equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with nonslip or slip boundary conditions. We prove that the strong solutions exists globally in time provided…
We consider temporal decay estimates for global solutions of the Navier-Stokes equations with the Coriolis force. We show that under several conditions including the smallness of the initial data, the solution decays as fast as the…
It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations…
Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible Navier{Stokes equations with no restrictions on…
We identify the leading term describing the behavior at large distances of the steady state solutions of the Navier-Stokes equations in 3D exterior domains with vanishing velocity at the spatial infinity.
The large time behavior of the unique strong solution to the barotropic compressible Navier-Stokes system is studied with large external forces and initial data, where the shear viscosity is a positive constant and the bulk one is…
In this paper, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes…
We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…
In this paper, we first obtain the temporal decay estimates for weak solutions to the three dimensional generalized Navier-Stokes equations. Then, with these estimates at disposal, we obtain the temporal decay estimates for higher order…