Related papers: Smooth or singular solutions to the Navier--Stokes…
This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have…
We prove that if $u$ is a suitable weak solution to the three dimensional Navier-Stokes equations from the space $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, then all scaled energy quantities of $u$ are bounded. As a consequence, it is…
This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
The existence of weak solutions to the stationary Navier-Stokes equations in the whole plane $\mathbb{R}^2$ is proven. This particular geometry was the only case left open since the work of Leray in 1933. The reason is that due to the…
We investigate the uniqueness of symmetric weak solutions to the stationary Navier-Stokes equation in a two-dimensional exterior domain $\Omega$. It is known that, under suitable symmetry condition on the domain and the data, the problem…
We consider the Navier-Stokes system in three dimensions perturbed by a transport noise which is sufficiently smooth in space and rough in time. The existence of a weak solution was proved recently, however, as in the deterministic setting…
We show the existence of strong solutions in Sobolev-Slobodetskii spaces to the stationary compressible Navier-Stokes equations with inflow boundary condition. Our result holds provided certain condition on the shape of the boundary around…
We establish various results concerning the uniqueness of zero velocity solutions for the static barotropic Navier--Stokes system. Some of them can be seen as Liouville-type theorems for problems in unbounded physical space.
Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in $\R^3$ with non-trivial swirl. Let $z$ denote the axis of symmetry and $r$ measure the distance to the z-axis. Suppose the solution satisfies either $|v…
In this paper, we investigate the incompressible steady Navier-Stokes system with no-slip boundary condition in a two-dimensional channel. Given any flux, the existence of solutions is proved as long as the width of cross-section of the…
In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…
We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…
We obtain the existence, regularity, uniqueness of the non-stationary problems of a class of non-Newtonian fluid is a power law fluid with $p>9/5$ in the half-space under slip boundary conditions.
We show the weak-strong uniqueness property for the compressible Navier-Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter…
We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary…
Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…
Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of…
We demonstrate existence in the ``large" and uniqueness in the ``small" of equilibrium configurations for the coupled system consisting of a Navier-Stokes fluid interacting with a rigid body subjected to spring forces and restoring moments.…
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not…