We show that the k-th eigenvalue of the Dirichlet Laplacian is strictly less than the k-th eigenvalue of the classical Stokes operator (equivalently, of the clamped buckling plate problem) for a bounded domain in the plane having a locally Lipschitz boundary. For a C boundary, we show that eigenvalues of the Stokes operator with Navier slip (friction) boundary conditions interpolate continuousl...

A variational approach is used to recover fluid motion governed by Stokes and Navier-Stokes equations. Unlike previous approaches where optical flow method is used to track rigid body motion, this new framework aims at investigating incompressible flows using optical flow techniques. We formulate a minimization problem and determine conditions under which unique solution exists. Numerical resul...

In this article, we study the steady generalized Navier-Stokes equations in a half-space in the setting of variable exponent spaces. We first establish variable exponent spaces of Clifford-valued functions in a half-space. Then, using this operator theory together with the contraction mapping principle, we obtain the existence and uniqueness of solutions to the stationary Navier-Stokes equation...

In this paper statistical solutions of the 3D Navier-Stokes-α model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-α model converge to statistical solutions of the exact 3D Navier-Stokes equations as α goes to zero. The statistical solutions considered here arise as families of time-projections of...

In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, using this renomalized equation we can give a new construction for a suitable weak solution of the classic...

Fluorescence line shapes and cooperative spontaneous emission in disordered one-dimensional molecular aggregates are calculated using closed expressions derived by applying the method of optimal fluctuation. A simple scaling relation Ls ∼ ωs is established between the low temperature disorder-induced Stokes shift ωs and the superradiance enhancement factor Ls. Scaling of the Stokes shift with a...

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has...

We consider the stochastic Stokes’ drift of a flexible dumbbell. The dumbbell consists of two isotropic Brownian particles connected by a linear string with zero natural length, and is advected by a sinusoidal wave. We find an asymptotic approximation for the Stokes’ drift in the limit of a weak wave, and find good agreement with the results of a Monte Carlo simulation. Interestingly, the depen...