Local Well-Posedness of the Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions [0.03%]
小初值下[公式见原文]维斜平均曲率流的局部适定性问题
Jiaxi Huang,Daniel Tataru
Jiaxi Huang
The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a ...
Stable Singularity Formation for the Keller-Segel System in Three Dimensions [0.03%]
Keller-Segel系统在三维空间中稳定的奇点形成
Irfan Glogić,Birgit Schörkhuber
Irfan Glogić
We consider the parabolic-elliptic Keller-Segel system in dimensions d≧3, which is the mass supercritical case. This system is known to exhibit rich dynamical behavior including singularity formation via self-similar solutions. An exp...
Fine Properties of Geodesics and Geodesic [Formula: see text]-Convexity for the Hellinger-Kantorovich Distance [0.03%]
Hellinger-Kantorovich距离的测地线及其Geoedesic [ Formula: see text ]-凸性性质
Matthias Liero,Alexander Mielke,Giuseppe Savaré
Matthias Liero
We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger-Kantorovich problem (HK), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new reg...
Weyl's Law for the Steklov Problem on Surfaces with Rough Boundary [0.03%]
带粗糙边界的曲面上Stecklov问题的Weyl定律
Mikhail Karpukhin,Jean Lagacé,Iosif Polterovich
Mikhail Karpukhin
The validity of Weyl's law for the Steklov problem on domains with Lipschitz boundary is a well-known open question in spectral geometry. We answer this question in two dimensions and show that Weyl's law holds for an even larger class of s...
The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles [0.03%]
德安-卡瓦瑟方程与扩散粒子系统中密度波动结构的关系
Federico Cornalba,Julian Fischer
Federico Cornalba
The Dean-Kawasaki equation-a strongly singular SPDE-is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the reg...
Existence of Radial Global Smooth Solutions to the Pressureless Euler-Poisson Equations with Quadratic Confinement [0.03%]
具二次约束项的压力无欧拉-泊松方程径向对称整体古典解的存在性
José A Carrillo,Ruiwen Shu
José A Carrillo
We consider the pressureless Euler-Poisson equations with quadratic confinement. For spatial dimension d≥2,d≠4, we give a necessary and sufficient condition for the existence of radial global smooth solutions, which is formulate...
Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential [0.03%]
具有大相互作用势的弱相互作用费米气体的相关能量
Niels Benedikter,Marcello Porta,Benjamin Schlein et al.
Niels Benedikter et al.
Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fo...
The Bulk-Boundary Correspondence for the Einstein Equations in Asymptotically Anti-de Sitter Spacetimes [0.03%]
渐近反德西特时空中的爱因斯坦方程的体界对应关系
Gustav Holzegel,Arick Shao
Gustav Holzegel
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes (M,g) with conformal boundary (I,g). We establish a correspondence, near I, between such spacetimes and their conformal boundary data on I. More specifically, given ...
Jia Shi
Jia Shi
In this paper, we show that if a solution to the Muskat problem in the case of different densities and the same viscosity is sufficiently smooth, then it must be analytic except at the points where a turnover of the fluids happens. ...
Stefano Borghini,Piotr T Chruściel,Lorenzo Mazzieri
Stefano Borghini
We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this, some new or improved tools are developed. These include a reverse Łojasiewicz inequality, which holds in a neighborhood of the extre...