Necessary conditions for spatial inviscid instability

Variational necessary and sufficient stability conditions for inviscid shear flow.

A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-self-adjoint eigenvalue problem) can be associated with positive eigenvalues of a certain self-adjoint ...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

New Necessary Conditions for

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...

On the Rayleigh-Taylor Instability for Incompressible, Inviscid Magnetohydrodynamic Flows

We study the Rayleigh-Taylor instabolity for two incompressible, immiscible, inviscid magnetohydrodynamic (MHD) fluids with zero resistivity, evolving with a free interface in the presence of a uniform gravitational field. We first construct the Rayleigh-Taylor steady-state solution with a denser fluid lying above the light one. Then, we turn to an analysis of the equations obtained from linear...

Transport and Instability for Incompressible and Inviscid Fluids

Incompressible perfect fluids are described by the Euler equations. We provide a new simple proof for well-posedness for velocities in C1;α and linear and nonlinear instability results using transport techniques. The results have an important consequence: the topology of C1;α is too fine for interesting questions about large time behavior.