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- Tarek M. Elgindi, Klaus Widmayer
- SIAM J. Math. Analysis
- 2015

We investigate some critical models for visco-elastic flows of Oldroyd-B type in dimension two. We use a transformation which exploits the Oldroyd-B structure to prove an L ∞ bound on the vorticity which allows us to prove global regularity for our systems.

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 note, using the ideas from our recent article [2], we prove strong ill-posedness for the 2D Euler equations in C k spaces. This note provides a significantly shorter proof of many of the main results in [1]. In the case k > 1 we show the existence of initial data for which the kth derivative of the velocity field develops a logarithmic singularity… (More)

We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the 2d incompressible Euler equations, thus making this problem amenable to an… (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)

- Peter Constantin, Tarek M. Elgindi, Mihaela Ignatova, Vlad Vicol
- J. Nonlinear Science
- 2017

We consider a model of electroconvection motivated by studies of the motion of a two dimensional annular suspended smectic film under the influence of an electric potential maintained at the boundary by two electrodes. We prove that this electroconvection model has global in time unique smooth solutions. May 1, 2016.

- Peter Constantin, Tarek M. Elgindi, Mihaela Ignatova, Vlad Vicol
- SIAM J. Math. Analysis
- 2017

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.