This paper is concerned with the global well-posedness and inviscid limits of several systems of Boussinesq equations with fractional dissipation. Three main results are proven. The first result assesses the global regularity of two systems of equations close to the critical 2D Boussinesq equations. This is achieved by examining their inviscid limits. The second result relates the global regula...

In a recent paper [11], Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B 2,1. In the present paper we prove that Navier-Stokes system is globally well-posed in B 2,1, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L is of order ν. keywords. navier-Stokes equations; Incom...

In this paper we present an intuitive explanation for the non-uniqueness of the traveling wave speed in the Fisher equation, showing a similar non-uniqueness property in the case of inviscid traveling waves. More precisely, we prove that traveling waves of the Fisher equation with wave speed c > 0 converges to the inviscid traveling wave with speed c > 0 as the diffusion vanishes. A complete di...

A pressure-based implicit procedure to solve the Euler and Navier-Stokes equations on a nonorthogonal mesh with collocated finite volume formulation is described. The boundedness criteria for this procedure are determined from Normalized Variable diagram (NVD) scheme.The procedure incorporates the ε−k eddy-viscosity turbulence model. The algorithm is tested for inviscid and turbulent transonic ...

Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction and that in transverse direction, if there is no work input. In this note, it is shown based on the energy gradient theory that inviscid nonuniform flow is uns...

We study the inviscid limit problem of the incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity ...

A simple model is presented for the analysis of inviscid flow fields over slender bodies accompanied by high rates of surface mass transfer. This model assumes a thin, inviscid injectant layer, which is separated from the outer flow by a contact discontinuity. Inviscid boundary-layer equations are shown to be applicable within the injectant layer, and the pressure gradient is found by matching ...

A general class of linear advective PDEs, whose leading order term is of viscous dissipative type, is considered. It is proved that beyond the limit of the essential spectrum of the underlying inviscid operator, the eigenvalues of the viscous operator, in the limit of vanishing viscosity, converge precisely to those of the inviscid operator. The general class of PDEs includes the equations of i...

Random dynamical models obtained as a perturbation of the GOY (GledzerOhkitani-Yamada) shell model for three-dimensional turbulence are defined. Both static (time-independent) and dynamical scaling properties of the randomly perturbed model are studied. The random static-inviscid manifold, in contrast to the dynamical evolution, does not show intermittent scaling laws. This behavior is linked t...