Related papers: Instability of Boost-invariant hydrodynamics with …
In this paper we prove a blow-up criterion for the compressible Navier-Stokes-Fourier system for general thermal and caloric equations of state with inhomogeneous boundary conditions for the velocity and the temperature. Assuming only that…
The paper discusses the similarities and the differences in the mathematical theories of the steady Boltzmann and incompressible Navier-Stokes equations posed in a bounded domain. First we discuss two different scaling limits in which…
This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…
We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $\omega^{(NS)} = 1 + \epsilon \omega$, set on the channel $\mathbb{T} \times [-1, 1]$, supplemented with Navier boundary conditions on the perturbation,…
In this paper, we investigate the vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier-Stokes equations with a slip boundary condition. We establish the local well-posedness of the strong solutions for initial boundary…
We propose inflow and outflow boundary conditions for the compressible Navier-Stokes equations and prove that they allow a priori estimates of the entropy, mass and total energy. Furthermore, we demonstrate how to approximate these boundary…
This paper is concerned with nonlinear stability of viscous contact discontinuity to inflow problem for the one-dimensional full compressible Navier-Stokes equations with different ends in half space $[0,\infty)$. For the case when the…
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary…
The one-dimensional non-boost-invariant evolution of the quark-gluon plasma, presumably produced during the early stages of heavy-ion collisions, is analyzed within the frameworks of viscous and anisotropic hydrodynamics. We neglect…
Relativistic Navier-Stokes equations express the conservation of the energy-momentum tensor and the particle number current in terms of the local hydrodynamic variables: temperature, fluid velocity, and the chemical potential. We show that…
We consider stability of non-rotating viscous gaseous stars modeled by the Navier-Stokes-Poisson system. Under general assumptions on the equations of states, we proved that the number of unstable modes for the linearized…
In this paper, the asymptotic-time behavior of solutions to an initial boundary value problem in the half space for 1-D isentropic Navier-Stokes system is investigated. It is shown that the viscous shock wave is stable for an impermeable…
This paper investigates the large-time behavior of a buoyancy-driven fluid without thermal diffusion under Navier-slip boundary conditions in a bounded domain with Lipschitz-continuous second derivatives. After establishing improved…
This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…
In this work we investigate the existence of weak solutions for steady flows of generalized incompressible and homogeneous viscous fluids. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the…
Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in $\R^3$ with non-trivial swirl. Such solutions are not known to be globally defined, but it is shown in \cite{MR673830} that they could only blow up on…
We study the high Reynolds number limit of a viscous fluid in the presence of a rough boundary. We consider the two-dimensional incompressible Navier-Stokes equations with Navier slip boundary condition, in a domain whose boundaries exhibit…
We obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity…
The present paper is concerned with an inviscid limit problem of radially symmetric stationary solutions for an exterior problem in $\mathbb{R}^n (n\ge 2)$ to compressible Navier-Stokes equation, describing the motion of viscous barotropic…