Related papers: Stability of Couette flow for 2D Boussinesq system…
The Boussinesq approximation is a cornerstone of geophysical fluid dynamics, yet its thermodynamic and energetic underpinnings have remained ambiguous. In standard formulations, the links with the fully compressible Navier--Stokes equations…
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…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…
For $\mathbb{R}^2$, the stability of smooth solutions of 2D anisotropic Boussinesq equations with horizontal dissipation is an open problem. In this work, we present a partial answer to this problem in a rougher function space…
We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by…
A thermal convection flow in the three-dimensional unbounded fluid domain exterior to a sphere is considered. The viscosity force is determined by a fractional power of the Stokes operator. A purely conductive steady state arises due to the…
We study dynamics of a coupled system consisting of the 3D Navier--Stokes equations which is linearized near a certain Poiseuille type flow in an (unbounded) domain and a classical (possibly nonlinear) elastic plate equation for transversal…
We present a new experimental set-up that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We…
This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…
This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable…
The stability of two-dimensional buoyancy-driven convection in a vertical porous slot, wherein a plane Couette flow is additionally present, is studied. This complex fluid flow scenario is examined under the influence of Robin-type boundary…
This paper investigates the asymptotic stability of rarefaction waves for a one-dimensional compressible fluid system, where the Newton's law of viscosity and Fourier's law of heat conduction are replaced by Maxwell's law and Cattaneo's…
We analyze the steady motion of a viscous incompressible fluid in a three-dimensional channel containing an obstacle through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by a fairly general datum and the…
We address the long time behavior of the Boussinesq system coupling the Navier-Stokes equations driven by density with the non-diffusive equation for the density. We construct solutions of the system justifying previously obtained a priori…
We prove the existence and uniqueness of strong solutions to the steady isentropic compressible Navier-Stokes equations with inflow boundary conditions for density and mixed boundary conditions for the velocity around a shear flow. In…
We consider a bi-dimensional viscous incompressible fluid in interaction with a beam located at its boundary. We show the existence of strong solutions for this fluid-structure interaction system, extending a previous result where we…
We consider solutions to the Navier-Stokes equations on $\mathbb{R}^2$ close to the Poiseuille flow with viscosity $0< \nu < 1$. For the linearized problem, we prove that when the $x$-frequency satisfy $|k| \ge \nu^{-\frac{1}{3}}$, the…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is…
The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and…