A note to the large-time behavior of a 3D chemotaxis-Navier-Stokes system with porous medium slow diffusion

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Large-time behavior of the weak solution to 3D Navier-Stokes equations

The weak solution to the Navier-Stokes equations in a bounded domain D ⊂ R3 with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t ≥ 0. In a bounded domain D the solution decays exponentially fast as t → ∞ if the force term decays at a suitable rate.

Author’s Reply to “A Note on the Simulation of Gas Diffusion in Capillaries and Porous Solids”

Author’s Reply to “A Note on the Simulation of Gas Diffusion in Capillaries and Porous Solids”

Global Large Solutions to 3-d Inhomogeneous Navier-stokes System with One Slow Variable

In this paper, we are concerned with the global wellposedness of 3-D inhomogeneous incompressible Navier-Stokes equations (1.2) in the critical Besov spaces with the norm of which are invariant by the scaling of the equations and under a nonlinear smallness condition on the isentropic critical Besov norm to the fluctuation of the initial density and the critical anisotropic Besov norm of the ho...