相关论文: An Inviscid Regularization for the Surface Quasi-G…
We study the temporal fluctuations of the flux of surface potential energy in Surface Quasi-Geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated…
By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the…
We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…
In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions…
We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of $\mathbb{R}^2$. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for…
We provide a variational construction of special solutions to the generalized surface quasi-geostrophic equations. These solutions take the form of N vortex patches with N-fold symmetry , which are steady in a uniformly rotating frame.…
The Thermal Quasi-Geostrophic (TQG) equation is a coupled system of equations that governs the evolution of the buoyancy and the potential vorticity of a fluid. It has a local in time solution as proved in [4]. In this paper, we give a…
We present a new regularized Oldroyd-B model in three dimensions which satisfies an energy estimate analogous to that of the standard model, and maintains the positive semi-definiteness of the conformation tensor. This results in the unique…
In this paper, we study the regularity of several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include stationary solutions, integral weak solutions, and viscosity…
We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a simplified vorticity stretching term and…
The Velocity-Vorticity (VV) formulation of the incompressible Navier-Stokes equations has become popular in recent years, especially in numerical studies, due to its structural advantages. Recently, with L. Rebholz, we introduced a Voigt…
We describe regularizing effects in the linearization of a kinetic equation that arises in study of a system of nonlinear waves satisfying the Schr\"odinger equation in terms of weak turbulence and condensate. The problem is first…
Turbulent behavior of the two-parameter family of generalized surface quasigeostrophic equations is examined both rigorously and numerically. We adapt a cascade mechanism argument to derive an energy spectrum that scales as…
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are $- \nu (- \triangle)^{\alpha} u$ and $- \kappa (-\triangle)^{\beta} b$. We show that smooth…
We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous degeneracy or/and singularity $$ \partial_t u=[|D u|^q+a(x,t)|D u|^s]\left(\Delta u+(p-2)\left\langle D^2 u\frac{D u}{|D u|},\frac{D u}{|D…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
In this paper, we study the generalized Proudman-Johnson equation posed on the torus. In the critical regime where the parameter $a$ is close to and slightly greater than 1, we establish finite time blow-up of smooth solutions to the…
For arbitrary values of a parameter $\lambda\in R$, finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for…
We prove the persistence of boundary smoothness of vortex patches for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations generalize the Euler equations by including an additional parameter, the Rossby radius…
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…