On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable Abstract. We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant γ > 3/2.

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Naiver-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of Q α, loc (R). This result applies to the usual incompressible Navier-Stokes equations and deduces a known link.

In this paper A Geometrical Design Method for Blade’s surface I in the impeller is provided here I is a solution to a coupling system consisting of the well-known Navier-Stokes equations and a four order elliptic boundary value problem . The coupling system is used to describe the relations between solutions of Navier-Stokes equations and the geometry of the domain occupied by fluids, and also ...

We introduce a construction of regular solutions to the Navier– Stokes equations which is specifically designed for the study of their asymptotic expansions. Using this construction, we give sufficient conditions for the convergence of those expansions. We also construct suitable normed spaces in which they converge. Moreover, in these spaces, the normal form of the Navier–Stokes equations asso...

We discuss the regularity of solutions of 2D incompressible NavierStokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear Fokker-Planck equation describing microscopic corpora embedded in the fluid. This leads naturally to bounded added stress and hence to W forcing of the Navier-Stokes equ...

In this paper, we present first-, second-, and third-order implicit finite-volume schemes for solving the Navier-Stokes equations on unstructured grids based on a hyperbolic formulation of the viscous terms. These schemes are first-, second-, and third-order accurate on irregular grids for both the inviscid and viscous terms and for all Reynolds numbers, not only in the primitive variables but ...

The numerical implementation of a multilevel finite element method for the steadystate Navier–Stokes equations is considered. The multilevel method proposed here for the Navier– Stokes equations is a multiscale method in which the full nonlinear Navier–Stokes equations are only solved on a single coarse grid; subsequent approximations are generated on a succession of refined grids by solving a ...

On Schwarz's domain decomposition methods for elliptic boundary value problems, submitted for publication, 1996. 6. M. J. Lai and P. Wenston, Bivariate spline method for numerical solution of steady state Navier-Stokes equations over polygons in stream function formulation, submitted, 1997. Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in

We consider an inverse problem of determining a spatially varying factor in a source term in a nonstationary linearized Navier-Stokes equations by observation data in an arbitrarily fixed sub-domain over some time interval. We prove the Lipschitz stability provided that the t-dependent factor satisfies a non-degeneracy condition. Our proof based on a new Carleman estimate for the Navier-Stokes ...