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...

Abstract The present paper studies the structure of set stationary solutions to incompressible Euler equations on rotating unit sphere that are near two basic zonal flows: Rossby–Haurwitz solution degree 2 and rigid rotation Y 1 ...

In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant L-metric on the group of volume-preserving diffeomorphisms of the flow domain. Here we propose geodesic, group-theoretic, and Hamiltonian frameworks to include fluid flows with vortex sheets. It turns out th...

Theoretical analyses are presented for the stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies under small perturbations in an inviscid incompressible flow at high angles of attack and sideslip. The three-dimensional problem of a pair of vortices over slender conical wings and bodies is reduced to a problem in two dimensions by using the conical flow assumpt...

In this paper, an unified high-order algorithm for all speeds is developed. The preconditioning matrix of Weiss and Smith combined with a 5th-order WENO scheme for inviscid flux and a fully conservative 4th order central differencing for viscous terms are employed. The unfactored implicit Gauss-Seidel relaxation scheme is used for time marching. The numerical simulation of a natural convective ...

This paper presents an Euler and boundary-layer method capable of unsteady flow and aeroelastic simulations. An integral boundary-layer solver is coupled with an Euler solver in a “semi-inverse” manner. For the inviscid part, approximate wall boundaryconditions are implemented on non-moving mean chord positions, whereas the full nonlinear Euler equation is solved in the field for accurate resol...

A numerical viscous/acoustic splitting approach for the calculation of an acoustic field is applied to study the sound generation by a pair of spinning vortices and by the unsteady interaction between an inviscid vortex and a finite length flexible boundary. Based on the unsteady hydrodynamic information from the known incompressible flow field, the perturbed compressible acoustic terms are cal...

This chapter is devoted to investigations of linear stability of plane-parallel flows of an inviscid nonheat-conducting vibrationally excited gas. Some classical results of the theory of linear stability of ideal gas flows, such as the first and second Rayleigh’s theorems and Howard’s theorem, are generalized. An equation of the energy balance of disturbances is derived, which shows that vibrat...

As V. I. Arnold observed in the 1960s, the Euler equations of incompressible fluid flow correspond formally to geodesic equations in a group of volume-preserving diffeomorphisms. Working in an Eulerian framework, we study incompressible flows of shapes as critical paths for action (kinetic energy) along transport paths constrained to be shape densities (characteristic functions). The formal geo...