Naturally the question of inviscid limit arises. Does the solution u of the CGL equation (1.1) tend to (in an appropriate space norm) the solution v of the NLS equation (1.2) as the parameters a and b tend to 0? What is the convergence rate? The answers are not immediate especially when the initial data for these equations are not smooth. Because of its importance in both mathematical theory an...

The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillations. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear s...

The paper addresses the dynamics of inviscid incompressible fluid confined within bounded domain with the inflow and outflow of fluid through certain parts of the boundary. This system is non-conservative essentially since the fluxes of energy and vorticity through the flow boundary are not equal to zero. Therefore, the dynamics of such flows should demonstrate the generic non-conservative phen...

The air cushioning effect in the gap between an almost inviscid body of water and a nearby solid wall (or another body of water) is studied theoretically and is found to depend on predominantly lubricating forces in the air, in certain applications. The situation in which the density and viscosity in air are taken as small compared with those in water is investigated. In this situation potentia...

A streamfunction-vorticity formulation is used to explore the extent to which turbulent and turbulently inviscid solutions to the mean momentum balance explain the mean flow across forest edges and within cavities situated inside dense forested canopies. The turbulent solution is based on the mean momentum balance where first-order closure principles are used to model turbulent stresses. The tu...

Abstract The aerodynamical optimal design (OD) of the shape of flying configurations (FCs) can be improved by refinements of its start software used for the optimization and of the optimization strategy itself. The author has two times enlarged the classical variational method. The first one consists in the inviscid global OD of the FC’s shape (the optimization of the camber, twist, thickness a...

We derive a time-dependent exact solution of the free surface problem for the Navier–Stokes equations that describes the planar extensional motion of a viscous sheet driven by inertia. The linear stability of the exact solution to oneand two-dimensional symmetric perturbations is examined in the inviscid and viscous limits within the framework of the long-wave or slender body approximation. Bot...

Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Laxor undercompressive-type shock waves of nonconservative hyperbolic systems with parabolic regularization. The hyperbolic equations may be of variable multiplicity and the parabolic regularizati...

Consider inviscid ‡uids in a channel f 1 < y < 1g. For the Couette ‡ow ~v0 = (y; 0), the vertical velocity of solutions to the linearized Euler equation at ~v0 decays in time. At the nonlinear level, such inviscid damping is widely open. First, we show that in any (vorticity) H s < 3 2 neighborhood of Couette ‡ow, there exist non-parallel steady ‡ows with arbitrary minimal horizontal period. Th...

We prove existence of global weak L solutions of the inviscid SQG equation in bounded domains.