Asymptotics Near Extinction for Nonlinear Fast Diffusion on a Bounded Domain [0.03%]
有界域上非线性快速扩散的渐近熄灭性质
Beomjun Choi,Robert J McCann,Christian Seis
Beomjun Choi
On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace is known to lead to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify th...
Jack Thomas,Huajie Chen,Christoph Ortner
Jack Thomas
We show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or...
The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion [0.03%]
相对论欧拉方程的物理真空边界条件：Hadamard局部适定性、弱解和延拓准则
Marcelo M Disconzi,Mihaela Ifrim,Daniel Tataru
Marcelo M Disconzi
In this paper we provide a complete local well-posedness theory for the free boundary relativistic Euler equations with a physical vacuum boundary on a Minkowski background. Specifically, we establish the following results: (i) local well-p...
Characterization of Minimizers of Aviles-Giga Functionals in Special Domains [0.03%]
特殊区域内Aviles-Giga泛函最小化的特征描述
Elio Marconi
Elio Marconi
We consider the singularly perturbed problem F ε ( u , Ω ) : = ∫ Ω ε | ∇ 2 u | 2 + ε - 1 | 1 - | ∇ u | 2 | 2 on bounded domains Ω ⊂ R 2 . Under appropriate boundary conditions, we ...
André Guerra,Lukas Koch,Sauli Lindberg
André Guerra
We consider the class of planar maps with Jacobian prescribed to be a fixed radially symmetric function f and which, moreover, fixes the boundary of a ball; we then study maps which minimise the 2p-Dirichlet energy in this class. We find a ...
Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics [0.03%]
回声链作为线性机制：范数膨胀，修改指数和渐近性
Yu Deng,Christian Zillinger
Yu Deng
In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be a (secondary) l...
Asymptotic Stability of Minkowski Space-Time with Non-compactly Supported Massless Vlasov Matter [0.03%]
非紧支撑无质量Vlasov物质的Minkowski时空的渐近稳定性
Léo Bigorgne,David Fajman,Jérémie Joudioux et al.
Léo Bigorgne et al.
We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov fie...
José A Carrillo,Young-Pil Choi
José A Carrillo
We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions...
Björn Gebhard,József J Kolumbán,László Székelyhidi Jr
Björn Gebhard
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the constituti...
Free Boundary Regularity for Almost Every Solution to the Signorini Problem [0.03%]
Signorini问题几乎每一个解的自由边界正则性
Xavier Fernández-Real,Xavier Ros-Oton
Xavier Fernández-Real
We investigate the regularity of the free boundary for the Signorini problem in R n + 1 . It is known that regular points are ( n - 1 ) -dimensional and C ∞ . However, even for C ∞ obstacles φ , the set of non-regular...