Related papers: Boundary layers and the vanishing viscosity limit …
In $1904$, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to $0$. His Ansatz was that the solution of Navier Stokes…
We study the stationary flow of incompressible micropolar fluid in a thin three-dimensional domain under Navier slip boundary condition for the velocity and no-spin condition for microrotation. After rescaling the governing equations, we…
We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a…
Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier-Stokes model cannot account for both features, and a simple…
In this paper we study a finite-depth layer of viscous incompressible fluid in dimension $n \ge 2$, modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…
We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of $N$-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The…
Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of \emph{incompressible} fluids is nowadays available not only for Navier--Stokes fluids but also for various…
In this paper we study the zero-viscosity limit of $2$-D Boussinesq equations with vertical viscosity and zero diffusivity, which is a nonlinear system with partial dissipation arising in atmospheric sciences and oceanic circulation. The…
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann…
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number…
Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $\Omega_{t +}, \Omega_{t -} \subset \mathbb{R}^N$, $N \ge 2$, where the domains are separated by a…
We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and…
We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected…
We study the vanishing viscosity limit for the three-dimensional incompressible Navier-Stokes equations in terms of the relative vorticity in the setting of axisymmetric velocity fields without swirl. We show that the weak convergence of…
We are concerned with the uniform regularity estimates and vanishing viscosity limit of solution to two dimensional viscous compressible magnetohydrodynamics (MHD) equations with transverse background magnetic field. When the magnetic field…
We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach…
Stationary flows of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb R^2$, periodic in the second and third variables, are considered. The flux and the Bernoulli function are prescribed at each…