A space–time variational approach to hydrodynamic stability theory

A space-time variational approach to hydrodynamic stability theory

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space-time variational formulation and associated generalized singular value decomposition of the (linearized) Navier-Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary or time-dependent base flows: we consider arbitrary disturbances in both the initial co...

Variational Approach to Retinex Theory

A New Variational Approach to the Stability of Gravitational Systems

We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are nonincreasing functions of their microscopic energy are nonlinearly stable by the ow. This was proved at the linear level by Antonov in 1961. Since then, sta...

Variational theory of two-fluid hydrodynamic modes at unitarity

We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau’s two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics p...

An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability

The solution of linear systems arising from the linear stability analysis of solutions of the Navier–Stokes equations is considered. Due to indefiniteness of the submatrix corresponding to the velocities, these systems pose a serious challenge for iterative solution methods. In this paper, the augmented Lagrangian-based block triangular preconditioner introduced by the authors in [2] is extende...