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We investiage the (slightly) super-critical 2-D Euler equations. The paper consists of two parts. In the first part we prove well-posedness in C s spaces for all s > 0. We also give growth estimates for the C s norms of the vorticity for 0 < s ≤ 1. In the second part we prove global regularity for the vortex patch problem in the super-critical regime.This(More)
For the 2D Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong to L ∞ ∩ H 1 but escapes H 1 immediately for t > 0. Our main observation is that a localized chunk of vorticity bounded in L ∞ ∩ H 1 with odd-odd symmetry is(More)
We compare the new still-image compression standard, JPEG2000, with two competing algorithms based on the Wavelet Difference Reduction (WDR) technique of encoding. Our comparison shows that these WDR methods provide far simpler encoding while also providing essentially the same performance as JPEG2000 at moderately high to very high compression ratios. They(More)
In this paper we formulate the equilibrium equation for a beam made of graphene subjected to some boundary conditions and acted upon by axial compression and nonlinear lateral constrains as a fourth-order nonlinear boundary value problem. We first study the nonlinear eigenvalue problem for buckling analysis of the beam. We show the solvability of the(More)
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 Navier-Stokes solutions remain bounded in L 2 t L ∞ x independently of the kinematic viscosity, and if they are equicontinuous at x2 = 0.