Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations [0.03%]
代数约束偏微分方程的低强制性及其在欧seen方程中的应用
Franz Achleitner,Anton Arnold,Volker Mehrmann
Franz Achleitner
The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts uniform...
Christian Bick,Davide Sclosa
Christian Bick
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and ...
Jane Allwright
Jane Allwright
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem....
Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity [Formula: see text] in Negative Sobolev Spaces [0.03%]
具有二次非线性的周期非线性Schrödinger方程在负Sobolev空间中的局部适定性[公式请参见文本]
Ruoyuan Liu
Ruoyuan Liu
We study low regularity local well-posedness of the nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity u ¯ 2 , posed on one-dimensional and two-dimensional tori. While the relevant bilinear estimate with respect to...
Computer-Assisted Proofs of Hopf Bubbles and Degenerate Hopf Bifurcations [0.03%]
计算机辅助证明Hopf泡泡和退化Hopf分岔
Kevin Church,Elena Queirolo
Kevin Church
We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate Hopf bifurcations in ordinary and delay differential equations. We apply the method to rigorously investigate these nonlocal orbit structures in t...
Regularization by Noise of an Averaged Version of the Navier-Stokes Equations [0.03%]
带噪声平均Navier-Stokes方程的正则性问题
Theresa Lange
Theresa Lange
In Tao 2016, the author constructs an averaged version of the deterministic three-dimensional Navier-Stokes equations (3D NSE) which experiences blow-up in finite time. In the last decades, various works have studied suitable perturbations ...
Travelling Waves in a PDE-ODE Coupled Model of Cellulolytic Biofilms with Nonlinear Diffusion [0.03%]
一类非线性扩散的菌藻共存模型的行波解问题研究
K Mitra,J M Hughes,S Sonner et al.
K Mitra et al.
We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value. Stabl...
Well-Posedness Properties for a Stochastic Rotating Shallow Water Model [0.03%]
随机旋转浅水模型的良posed性性质分析
Dan Crisan,Oana Lang
Dan Crisan
In this paper, we study the well-posedness properties of a stochastic rotating shallow water system. An inviscid version of this model has first been derived in Holm (Proc R Soc A 471:20140963, 2015) and the noise is chosen according to the...
Second Order Splitting Dynamics with Vanishing Damping for Additively Structured Monotone Inclusions [0.03%]
具有消失阻尼的二阶分裂动力学用于加性结构单值包含问题
Radu Ioan Boţ,David Alexander Hulett
Radu Ioan Boţ
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator A and a cocoercive operator B. We study the asymptotic behaviour of the trajectories generated by a second ord...
Balázs Boros,Josef Hofbauer
Balázs Boros
Whereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examp...