Related papers: Free Boundary Problem for inhomogeneous Navier-Sto…
We present an exact solution for the time-dependent Stokes problem of an infinite cylinder of radius r=a in a fluid with harmonic boundary conditions at infinity. This is a 3-dimensional problem but, because of translational invariance…
In this paper, we consider a free boundary problem of a semilinear nonhomogeneous elliptic equation with Bernoulli's type free boundary. The existence and regularity of the solution to the free boundary problem are established by use of the…
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the…
We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded multiply connected domain. We prove that this problem has a solution in some…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the…
We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian operator (--$\Delta$) $\alpha$/2 in the diffusion term. In the…
We study regularity criteria for the $d$-dimensional incompressible Navier-Stokes equations. We prove if $u\in L_{\infty}^tL_d^x((0,T)\times \mathbb{R}^d_+)$ is a Leray-Hopf weak solution vanishing on the boundary and the pressure $p$…
We study a free-boundary fluid-structure interaction problem with growth, which arises from the plaque formation in blood vessels. The fluid is described by the incompressible Navier-Stokes equation, while the structure is considered as a…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
$H^2$-spatial regularity of stationary and non-stationary problems for Bingham fluids formulated with the pseudo-stress tensor is discussed. The problem is mathematically described by an elliptic or parabolic variational inequality of the…
We consider the inhomogeneous incompressible Navier-Stokes system in a smooth two or three dimensional bounded domain, in the case where the initial density is only bounded. Existence and uniqueness for such initial data was shown recently…
Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…
A numerical method for the two-dimensional, incompressible Navier--Stokes equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving…
The paper compares standard iterative methods for solving the generalized Stokes problem arising from the time and space approximation of the time-dependent incompressible Navier-Stokes equations. Various preconditioning techniques are…
Consider a rigid body ${\mathcal S} \subset {\mathbb R}^3$ immersed in an infinitely extended Navier-Stokes liquid and the motion of the body-fluid interaction system described from a reference frame attached to ${\mathcal S}$. We are…
We give the first mathematical construction of two-dimensional traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations for a single finite depth layer of constant density fluid. Our construction is based on…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…
We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $\mathbb{R}^d$ (with $d\geq2$). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global…