Related papers: An Inviscid Regularization for the Surface Quasi-G…
The shear viscosity of the quark-gluon plasma (QGP) plays a crucial role in interpreting current measurements from heavy-ion collisions and is a key input to hydro-dynamical models. The interest in shear viscosity also lies in the fact that…
In the present paper, we study the fast rotation and inviscid limits for the 2-D dissipative surface quasi-geostrophic equation with a dispersive forcing term $A \mathcal{R}_{1} \vartheta$, in the domain $\Omega =\mathbb{T}^{1} \times…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
We obtain up to a flat boundary regularity results in parabolic H\"{o}lder spaces for viscosity solutions of fully nonlinear parabolic equations with oblique boundary conditions.
In this work we construct global unique solutions of the dissipative Surface quasi-geostrophic equation ($\alpha$-SQG) that lose regularity instantly when there is super-critical fractional diffusion.
We prove that weak solutions of a slightly supercritical quasi-geostrophic equation become smooth for large time. We prove it using a De Giorgi type argument using ideas from a recent paper by Caffarelli and Vasseur.
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic…
In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…
This paper deals with the optimal regularity for entropy solutions of conservation laws. For this purpose, we use two key ingredients: (a) fine structure of entropy solutions and (b) fractional $BV$ spaces. We show that optimality of the…
In this article, the authors prove the existence of global weak solutions to the inviscid three-dimensional quasi-geostrophic equation. This equation models the evolution of the temperature on the surface of the earth. It is widely used in…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…
We show at the PDE level that the monolithic parabolic regularization of the equations of ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfills the minimum entropy principle, and preserves the…
The linear normal-mode stratorotational instability (SRI) is analytically reexamined in the inviscid limit where the length scales of horizontal disturbances are large compared their vertical and radial counterparts. Boundary conditions…
In this paper we address the existence of time periodic solutions for the generalized inviscid SQG equation in the unit disc with homogeneous Dirichlet boundary condition when $\alpha\in (0,1)$. We show the existence of a countable family…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares…
We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in $\mathbb R^3$, as well as a related weighted model. The well-posedness of weak solutions for…
In this paper, we investigate the existence of a finite number of vortex patches for the generalized surface quasi-geostrophic (gSQG) equations with $\alpha \in [1,2)$, focusing on configurations that may rotate uniformly, translate, or…