This paper evaluates the use of the compressible Navier-Stokes equations, with prescribed zero velocities, as a model for heat transfer in solids. In particular in connection with conjugate heat transfer problems. We derive estimates, and show how to choose and scale the coefficients of the energy part in the Navier-Stokes equations, such that the difference between the energy equation and the ...

We present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced Navier Stokes equations in R. The method, based on so-called Gevrey estimates, also yields explicit bounds on the growth of the radius of analyticity of the solution in time. Moreover, under the assumption that the Navier Stokes solution stays sufficiently close to a solution of th...

This paper is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic uids in the whole space R d (d = 2 or 3). This problem was investigated by P.L. Lions and N. Masmoudi 19]. We present here a diierent approach based upon Strichartz' estimates for the linear wave equation like in 21] in the inviscid case, which improves the convergence...

We present a nonlinear model predictive framework for closedloop control of two-phase flows governed by the Cahn-Hilliard NavierStokes system. We adapt the concept for instantaneous control from [6, 12, 16] to construct distributed closed-loop control strategies for twophase flows. It is well known that distributed instantaneous control is able to stabilize the Burger’s equation [16] and also t...

We prove existence of weak solutions of stochastic Navier-Stokes equations in R which do not satisfy the coercivity condition. The equations are formally derived from the critical point of some variational problem defined on the space of volume preserving diffeomorphisms in R. Since the domain of our equation is unbounded, it is more difficult to get tightness of approximating sequences of solu...

We establish a Navier–Stokes–Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of DiPerna–Lions renormaliz...

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations of the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about arbitrary, far-from-equilibrium reference states. The primary result is a set of ...

We investigates the global regularity issue concerning a model equation proposed by Hou and Lei [3] to understand the stabilizing effects of the nonlinear terms in the 3D axisymmetric Navier-Stokes and Euler equations. Two major results are obtained. The first one establishes the global regularity of a generalized version of their model with a fractional Laplacian when the fractional power sati...

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p + 1 dimensions, there is a uniquely associated “dual” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “n...

In this paper, the unsteady Navier-Stokes Takagi-Sugeno (T-S) fuzzy equations (UNSTSFEs) are represented as a differential algebraic system of strangeness index one by applying any spatial discretization. Since such differential algebraic systems have a difficulty to solve in their original form, most approaches use some kind of index reduction. While processing this index reduction, it is impo...