相关论文: Non-existence of splash singularities for the two-…

We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…

We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…

We consider the inviscid limit for the two-dimensional Navier--Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier--Stokes and Euler velocity fields vanishes in…

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's…

We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…

We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $\Omega$. We show the convergence of the weak solution to the…

In this paper we consider the Cauchy problem for the 3D Navier-Stokes equations for incompressible flows. The initial data are assumed to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solutions can…

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…

We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a~priori…

We study a nonlinear coupled fluid-structure system modelling the blood flow through arteries. The fluid is described by the incompressible Navier-Stokes equations in a 2D rectangular domain where the upper part depends on a structure…

The stability of an irreversible singularity, such as a Riemann shock to the full Euler system, in the absence of any technical conditions on perturbations, remains a major open problem even within mono-dimensional framework. A natural…

Singular vorticty solutions of the incompressible 3D-Euler equation are constructed which satisfy the BKM criterion (cf. [2]). The construction is done by inviscid limits of vorticity solutions of transformed incompressible Navier Stokes…

Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders…

In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e. that the curve touches itself either in a point or…

There are a few examples of solutions to the incompressible Euler equations which are piecewise smooth with a discontinuity of the tangential velocity across a hypersurface evolving in time: the so-called vortex sheets. An important open…

The forced 2D Euler equations exhibit non-unique solutions with vorticity in $L^p$, $p > 1$, whereas the corresponding Navier-Stokes solutions are unique. We investigate whether the inviscid limit $\nu \to 0^+$ from the forced 2D…

For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the…

We consider the Riemann problem composed of two shocks for the 1D Euler system. We show that the Riemann solution with two shocks is stable and unique in the class of weak inviscid limits of solutions to the Navier-Stokes equations with…