Related papers: $\Gamma$-convergence for nearly incompressible flu…
This paper is concerned with the mathematical derivation of the inhomoge-neous incompressible Navier-Stokes equations (INS) from the compressible Navier-Stokes equations (CNS) in the large volume viscosity limit. We first prove a result of…
In this paper we study the dimension reduction limits of the compressible Navier--Stokes equations over product Riemannian manifolds $\mathcal{O}_\epsilon \cong \mathcal{M} \times \epsilon\mathcal{F}$, such that $\dim\,(\mathcal{M})=n$ and…
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…
For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such…
We consider a general compressible, viscous, heat and magnetically conducting fluid described by the compressible Navier-Stokes-Fourier system coupled with induction equation. In particular, we do not assume conservative boundary conditions…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…
In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity $\omega_0$ and the circulation $\gamma$ of the initial flow around the obstacle. We…
The compressible Navier-Stokes system with the constant viscosity and the nonlinear heat conductivity which is proportional to a positive power of the temperature and may be degenerate is considered. Under the outer pressure boundary…
We consider an alternative Navier-Stokes model for compressible viscous ideal gases, originally proposed in \cite{Svard18}. We derive a priori estimates that are sufficiently strong to support a weak entropy solution of the system. Guided…
The chemotaxis--Navier--Stokes system \begin{equation*}\label{0.1} \left\{\begin{array}{ll} n_t+u\cdot \nabla n=\triangle n-\chi\nabla\cdotp \left(\displaystyle\frac n {c}\nabla c\right)+n(r-\mu n), c_t+u\cdot \nabla c=\triangle c-nc, u_t+…
We consider the incompressible Navier-Stokes equations in the cylinder $\R \times \T$, with no exterior forcing, and we investigate the long-time behavior of solutions arising from merely bounded initial data. Although we do not know if…
In this paper, we provide rigorous justification of the hydrostatic approximation and the derivation of primitive equations as the small aspect ratio limit of the incompressible three-dimensional Navier-Stokes equations in the anisotropic…
In this paper, we perform the fast rotation limit $\varepsilon\rightarrow0^+$ of the density-dependent incompressible Navier-Stokes-Coriolis system in a thin strip…
Recently, A. Vasseur and C. Yu have proved the existence of global entropy-weak solutions to the compressible Navier-Stokes equations with viscosities $\nu(\varrho)=\mu\varrho$ and $\lambda(\varrho)=0$ and a pressure law under the form…
In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex. Thanks to the elementary lemma…
We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in $3-D$. We show that as $\lambda\to 0$ the velocity field $u^{\lambda}$ strongly…
In the diffusive regime, we obtain the uniform in Knudsen number estimate on the two-species Vlasov-Maxwell-Landau system with Coulomb potential around the global equilibrium. As a consequence, we justify the limit to the two-fluid…
We prove a global-in-time limit from the two-species Vlasov-Maxwell-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. Besides the techniques developed for the classical solutions to the…