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We address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the…
We deal with the barotropic compressible Navier-Stokes equations subject to large external potential forces with slip boundary condition in a 3D simply connected bounded domain, whose smooth boundary has a finite number of 2D connected…
We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application…
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…
A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control problem is proved and the first-order optimality conditions are…
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…
We consider the solution to the 2D Navier-Stokes equations around the Poiseuille flow $(y^2,0)$ on $\mathbb{T}\times\mathbb{R}$ with small viscosity $\nu>0$. Via a hypocoercivity argument, we prove that the $x-$dependent modes of the…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface, despite the assumption of the no-slip condition is preferred to avoid boundary terms in the analysis…
We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each…
This paper focuses on the so-called Weighted Inertia-Dissipation-Energy (WIDE) variational approach for the approximation of unsteady Leray-Hopf solutions of the incompressible Navier-Stokes system. Initiated in [56], this variational…
In the present paper, we study the uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system whose viscosity and heat conductivity are allowed to vanish at different order. The problem is studied in a…
The objective of this work is to present the existence result for the evolu- tionary compressible Navier-Stokes equations via time discretization. We consider the two-dimensional case with slip boundary conditions. First, the existence of…
We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with…
We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain $\Omega…
The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework has been addressed in [7] more than fifteen years ago. However, whether (optimal) time-decay rates could be shown in…
We consider a multi-dimensional model of a compressible fluid in a bounded domain. We want to estimate the density and velocity of the fluid, based on the observations for only velocity. We build an observer exploiting the symmetries of the…
We consider the motion of a compressible, viscous, and heat conducting fluid in the regime of small viscosity and heat conductivity. It is shown that weak solutions of the associated Navier- Stokes-Fourier system converge to a (strong)…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
In some problems of fluid mechanics, it is possible to be confronted with data that are not regular, that is why we are interested here in the search for the so-called very weak solutions for the stationary Stokes problem with Navier-type…