Related papers: Antithesis of the Stokes paradox on the hyperbolic…
We show that non-uniqueness of the Leray-Hopf solutions of the Navier--Stokes equation on the hyperbolic plane observed in arXiv:1006.2819 is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on the…
We develop the asymptotic behavior for the solutions to the stationary Navier-Stokes equation in the exterior domain of the 2D hyperbolic space. More precisely, given the finite Dirichlet norm of the velocity, we show the velocity decays to…
This paper provides asymptotic structure at spatial infinity of plane steady Stokes flow in exterior domains when the obstacle is rotating with constant angular velocity. The result shows that there is no longer Stokes paradox due to the…
We study solutions to the obstacle problem for the stationary Navier--Stokes system in a~two dimensional exterior domain (flow past a prescribed body). We prove that the classical Leray solution to this problem is always nontrivial. No…
We study the nonhomogeneous boundary value problem for the Navier--Stokes equations of steady motion of a viscous incompressible fluid in a three--dimensional exterior domain with multiply connected boundary. We prove that this problem has…
We consider the Navier-Stokes equation on $\mathbb{H}^{2}(-a^{2})$, the two dimensional hyperbolic space with constant sectional curvature $-a^{2}$. We prove an ill-posedness result in the sense that the uniqueness of the Leray-Hopf weak…
The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in $\mathbb{R}^2$. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence…
We establish the existence of a solution to the Navier-Stokes equations on a moving domain with surface tension in an optimal Sobolev space for the case of two space dimension. No compatibility conditions are required to guarantee the…
A hyperbolic relaxation of the classical Navier-Stokes problem in 2D bounded domain with Dirichlet boundary conditions is considered. It is proved that this relaxed problem possesses a global strong solution if the relaxation parameter is…
The problem for the stationary Navier-Stokes equation in 3D under finite Dirichlet norm is open. In this paper we answer the analogous question on the 3D hyperbolic space. We also address other dimensions and more general manifolds.
In this paper, we investigate the nonhomogeneous boundary value problem for the steady Navier-Stokes equations in a helically symmetric spatial domain. When data is assumed to be helical invariant and satisfies the compatibility condition,…
The Leray-Hopf solutions to the Navier-Stokes equation are known to be unique on $\R^{2}$. In our previous work we showed the breakdown of uniqueness in a hyperbolic setting. In this article, we show how to formulate the problem in order so…
This study is devoted to the incompressible and stationary Navier-Stokes equations in two-dimensional unbounded domains. First, the main results on the construction of the weak solutions and on their asymptotic behavior are reviewed and…
We study solutions to stationary Navier Stokes system in two dimensional exterior domain. We prove that any such solution with finite Dirichlet integral converges at infinity uniformly. No additional condition (on symmetry or smallness) are…
We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in…
In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain satisfying the geometrical control condition the system…
This paper proposes a solution to Stokes' paradox for asymptotically uniform viscous flow around a cylinder. The existence of a {\it global} stream function satisfying a perturbative form of the two-dimensional Navier-Stokes equations for…
We prove new existence and uniqueness results in full Sobolev spaces for the steady-state Oseen problem in a smooth exterior domain of $\mathbb{R}^n$, $n\ge 2$. These results are then employed, on the one hand, in the study of analogous…
We consider the stationary incompressible Navier Stokes equation in the exterior of a disk B with non-zero Dirichlet boundary conditions on the disk and zero boundary conditions at infinity. We prove the existence of solutions for an open…
In this paper, we study a hyperbolic version of the Navier-Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl…