Dirk Hundertmark,Michal Jex,Markus Lange
Dirk Hundertmark
In the present paper we study two challenging problems for helium-type systems: the existence of eigenvalues at thresholds and the asymptotic behavior of the corresponding eigenfunctions. Since the usual methods for addressing these problem...
Stability of Rayleigh-Jeans Equilibria in the Kinetic FPU Equation [0.03%]
Kinetic FPU方程中Rayleigh-Jeans平衡的稳定性
Pierre Germain,Joonhyun La,Angeliki Menegaki
Pierre Germain
We study the nonlinear dynamics of the kinetic wave equation associated with the FPU problem and prove the stability of the non-singular Rayleigh-Jeans equilibria. The lack of a spectral gap for the linearized problem leads to polynomial de...
Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics [0.03%]
气体动力学欧拉系统的最大耗散性和适定性问题
Eduard Feireisl,Ansgar Jüngel,Mária Lukáčová-Medvid&#x;ová
Eduard Feireisl
We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two-...
Maarten V de Hoop,Matti Lassas,Jinpeng Lu et al.
Maarten V de Hoop et al.
We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress...
Sebastian Herr,Robert Schippa,Nikolay Tzvetkov
Sebastian Herr
We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these in hand, we show that gl...
Finite Time Blow-Up for the Hypodissipative Navier Stokes Equations with a Force in [Formula: see text] [0.03%]
带力的临界拟耗散Navier-Stokes方程解的整体存在性与爆破准则
Diego Córdoba,Luis Martínez-Zoroa,Fan Zheng
Diego Córdoba
In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by | ∇ | α for any α ∈ [ 0 , 	...
Zachary P Adams,Maximilian Engel,Rishabh S Gvalani
Zachary P Adams
We study metastable behaviour in systems of weakly interacting Brownian particles with localised, attractive potentials which are smooth and globally bounded. In this particular setting, numerical evidence suggests that the particles conver...
Long-Time Dynamics for the Kelvin-Helmholtz Equations Close to Circular Vortex Sheets [0.03%]
接近圆形涡环的Kelvin-Helmholtz方程的长时间动态性
Federico Murgante,Emeric Roulley,Stefano Scrobogna
Federico Murgante
We consider the Kelvin-Helmholtz system describing the evolution of a vortex-sheet near the circular stationary solution. Answering previous numerical conjectures in the 1990s physics literature, we prove an almost global existence result f...
Verena Bögelein,Frank Duzaar,Giulia Treu
Verena Bögelein
We establish the existence of Lipschitz-continuous solutions to the Cauchy-Dirichlet problem for a class of evolutionary partial differential equations of the form ∂ t u - div x ∇ ξ f ( ∇ u ) = 0 in a spac...
Long-Time Stability of a Stably Stratified Rest State in the Inviscid 2D Boussinesq Equation [0.03%]
二维无粘Boussinesq方程稳定层结平衡态的长时间稳定性分析
Catalina Jurja,Klaus Widmayer
Catalina Jurja
We establish the nonlinear stability on a timescale O ( ε - 2 ) of a linearly, stably stratified rest state in the inviscid Boussinesq system on R 2 . Here, ε > 0 denotes the size of an initially sufficiently small, Sobolev r...