Related papers: Asymptotics of solutions for a basic case of fluid…

In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…

We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…

This paper extends the weak solution theory for the 3D Navier-Stokes equations of Barker, Seregin and Sverak from a critical setting to a supercritical setting making sure to include a useful a priori energy bound as well as a statement…

In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…

We show existence and uniqueness of regular time-periodic solutions to the Navier-Stokes problem in the exterior of a rigid body, $\mathscr B$, that moves by arbitrary (sufficiently smooth) time-periodic translational motion of the same…

We consider the asymptotic behavior as time goes to infinity of the $L^{2}$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\bf R}^{n}$ ($n \geq 2$). As an application we shall study the optimality of the…

Center-manifold approximations for infinite-dimensional systems are treated in the context of the Navier--Stokes equations extended to include an equation for the parameter evolution. The consequences of system extension are non-trivial and…

In this paper we shall consider the Navier-Stokes equations in the half plane with Euler-type initial conditions, i.e. initial conditions which have a non-zero tangential component at the boundary. Under analyticity assumptions for the…

We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

An alternative form of the general solution of the linearized stationary Navier-Stokes equations for an incompressible fluid in spherical coordinates is obtained by the vector potential method. A previously published solution to this…

We study the long-time dynamics of the Navier-Stokes equations in the three-dimensional periodic domains with a body force decaying in time. We introduce appropriate systems of decaying functions and corresponding asymptotic expansions in…

For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…

We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) elastic plate equation for transversal displacement on a flexible flat part of the…

Axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and he angular components of the velocity and vorticity are assumed to vanish. If the norm…

In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…

We enable a theory of intrinsic asymptotic expansions for the steady state solutions of the full Navier-Stokes equations. Such a theory was first developed in Foias et al (2024 Commun. Pure Appl. Anal. 23, 269-303) for Galerkin…

Let $D$ be the exterior of a cone inside a ball, with its altitude angle at most $\pi/6$ in $\mathbb{R}^3$, which touches the $x_3$ axis at the origin. For any initial value $v_0 = v_{0,r}e_{r} + v_{0,\theta} e_{\theta} + v_{0,3} e_{3}$ in…

We consider weak (''Leray'') solutions to the stationary Navier-Stokes system with Oseen and rotational terms, in an exterior domain. It is shown the velocity may be split into a constant times the first column of the fundamental solution…

We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the…

We cope with a free boundary fluid-structure interaction model. In the model, the viscous incompressible fluid interacts with elastic body via the common boundary. The motion of the fluid is governed by Navier-Stokes equations while the…