Zobrazeno 1 - 10
of 130
pro vyhledávání: '"Elgindi, Tarek M."'
Fix a bounded, analytic, and simply connected domain $\Omega\subset\mathbb{R}^2.$ We show that all analytic steady states of the Euler equations with stream function $\psi$ are either radial or solve a semi-linear elliptic equation of the form $\Delt
Externí odkaz:
http://arxiv.org/abs/2408.14662
Autor:
Bianchini, Roberta, Elgindi, Tarek M.
We consider equations of the type: \[\partial_t \omega = \omega R(\omega),\] for general linear operators $R$ in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localized solutions. S
Externí odkaz:
http://arxiv.org/abs/2407.16450
We introduce a local-in-time existence and uniqueness class for solutions to the 2d Euler equation with unbounded vorticity. Furthermore, we show that solutions belonging to this class can develop stronger singularities in finite time, meaning that t
Externí odkaz:
http://arxiv.org/abs/2312.17610
We develop a computer-assisted symbolic method to show that a linearized Boussinesq flow in self-similar coordinates gives rise to an invertible operator.
Comment: The argument involves 7 Matlab files, which are attached to this submission
Comment: The argument involves 7 Matlab files, which are attached to this submission
Externí odkaz:
http://arxiv.org/abs/2310.19781
We establish finite-time singularity formation for $C^{1,\alpha}$ solutions to the Boussinesq system that are compactly supported on $\mathbb{R}^2$ and infinitely smooth except in the radial direction at the origin. The solutions are smooth in the an
Externí odkaz:
http://arxiv.org/abs/2310.19780
Autor:
Elgindi, Tarek M., Liss, Kyle
We construct a divergence-free velocity field $u:[0,T] \times \mathbb{T}^2 \to \mathbb{R}^2$ satisfying $$u \in C^\infty([0,T];C^\alpha(\mathbb{T}^2)) \quad \forall \alpha \in [0,1)$$ such that the corresponding drift-diffusion equation exhibits anom
Externí odkaz:
http://arxiv.org/abs/2309.08576
Autor:
Elgindi, Tarek M.
It is well-known that the first energy shell, \[\mathcal{S}_1^{c_0}:=\{\alpha \cos(x+\mu)+\beta\cos(y+\lambda): \alpha^2+\beta^2=c_0\,\, \&\,\, (\mu,\lambda)\in\mathbb{R}^2\}\] of solutions to the 2d Euler equation is Lyapunov stable on $\mathbb{T}^2
Externí odkaz:
http://arxiv.org/abs/2307.12290
Publikováno v:
Invent. math. (2024)
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to establish a n
Externí odkaz:
http://arxiv.org/abs/2305.09582
We consider the advection-diffusion equation on $\mathbb{T}^2$ with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale $|\log \nu|$, where $\nu$ is the
Externí odkaz:
http://arxiv.org/abs/2304.05374