For the purpose of engineering, it is important to study convergent rates in process low Mach number limit. However, there are only a few results on this issue, which focus cases isentropic regime or ones without solid boundaries. In paper, we obtain convergence for local strong solutions non-isentropic compressible Navier-Stokes equations with well-prepared initial data and Navier-slip boundar...

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in half-space $$\mathbb{R}_+^3$$ is rigorously proved under Navier-slip boundary condition for velocity and Dirichlet electric potential. This achieved by establishing nonlinear stability approximation solutions involving strong layer density potential, which comes from br...

Abstract. We investigate a kinetic model for the sedimentation of dilute suspensions of rod-like particles under gravity, deduced by Helzel, Otto and Tzavaras (2011), which couples the impressible (Navier-)Stokes equation with the Fokker-Planck equation. With no-flux boundary condition for distribution function, we establish the existence and uniqueness of global weak solution to the two dimens...

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three–dimensional Navier–Stokes equations in the whole space, as well as for the case of periodic boundary conditions. AMS Subject Classifications: 35Q35, 65M70

We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists incompressible Navier-Stokes equations two immiscible fluids standard interface conditions, Navier slip condition along solid wall, and a angle which relates dynamic to normal velocity line (Ren et al. (2010) \cite{Ren10}). In method, go...

We show that the continuous (in time) form of the projection-3 scheme proposed in [2] is not a proper approximation of the unsteady Navier-Stokes equations. Hence the projection-3 scheme and its variants are not appropriate for the numerical computation of the Navier-Stokes equations. The projection-3 scheme in [2] was proposed as a possible improvement over the projection-1 and projection-2 sc...

We consider the Navier–Stokes equations in a thin domain of which the top and bottom are not flat. The velocity fields are subject to the Navier conditions on those boundaries and the periodicity condition on the other sides on the domain. The model arises from studies of climate and oceanic flows. We show that the strong solutions exist for all time provided the initial data belong to a “large...

This paper is aiming at obtaining weak solution for a bi-nonlocal fourth order elliptic problem with Navier boundary condition. Our approach based on variational methods and critical point theory.