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Related papers: Symplectic nonsqueezing of the KdV flow

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We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…

Optimization and Control · Mathematics 2025-07-17 Lénaïc Chizat , Maria Colombo , Xavier Fernández-Real

To what extent can the one-dimensional slim disk model reproduce the multi-dimensional results of global radiation-hydrodynamic simulations of super-Eddington accretion? With this question in mind, we perform systematic simulation study of…

High Energy Astrophysical Phenomena · Physics 2018-11-07 Takaaki Kitaki , Shin Mineshige , Ken Ohsuga , Tomohisa Kawashima

We show approximate controllability of Boussinesq flows in $\mathbb{T}^2 = \mathbb{R}^2 / 2\pi\mathbb{Z}^2$ driven by finite-dimensional controls that are supported in any fixed region $\omega \subset \mathbb{T}^2$. This addresses a…

Analysis of PDEs · Mathematics 2025-10-01 Manuel Rissel

A variable-coefficient forced Korteweg-de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of…

Pattern Formation and Solitons · Physics 2017-01-18 Xin Yu , Zhi-Yuan Sun , Kai-Wen Zhou , Yu-Jia Shen

We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of…

Geometric Topology · Mathematics 2022-02-15 Pablo Suárez-Serrato

We give an explicit formula for the Gromov width for a class of symplectic toric manifolds constructed from simple graphs. As a corollary, we show a version of non-squeezing theorem with respect to the inclusion of connected graphs.

Symplectic Geometry · Mathematics 2020-11-20 Suyoung Choi , Taekgyu Hwang

We provide a derivative estimate for the pluriclosed flow, controlling higher order derivatives of Chern curvature and torsion using the Chern curvature. Moreover, we derive an estimate for torsion tensor using Chern Ricci curvature in…

Differential Geometry · Mathematics 2023-11-14 Yanan Ye

We study the orthogonal projections of symplectic balls in $\mathbb{R}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a…

Symplectic Geometry · Mathematics 2024-05-20 Nuno Costa Dias , Maurice A. de Gosson , Joao Nuno Prata

Non-invertible symmetries have recently been understood to provide interesting contraints on RG flows of QFTs. In this work, we show how non-invertible symmetries can also be used to generate entirely new RG flows, by means of so-called…

High Energy Physics - Theory · Physics 2022-08-24 Justin Kaidi , Gabi Zafrir , Yunqin Zheng

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…

Numerical Analysis · Mathematics 2007-05-23 Sebastien Zimmermann

We prove the asymptotic stability of shear flows close to the Couette flow for the 2-D inhomogeneous incompressible Euler equations on $\mathbb{T}\times \mathbb{R}$. More precisely, if the initial velocity is close to the Couette flow and…

Analysis of PDEs · Mathematics 2023-03-28 Qi Chen , Dongyi Wei , Ping Zhang , Zhifei Zhang

We propose a finite volume stochastic collocation method for the random Euler system. We rigorously prove the convergence of random finite volume solutions under the assumption that the discrete differential quotients remain bounded in…

Numerical Analysis · Mathematics 2026-01-01 Maria Lukacova-Medvidova , Simon Schneider

Recently Ricca and Maggione [MHD (2008)] have presented a very simple and interesting model of stretch-twist-fold dynamo in diffusive media based on numerical simulations of Riemannian flux tubes. In this paper we present a yet simpler way…

Fluid Dynamics · Physics 2009-04-13 Garcia de Andrade

In this paper, we construct a simple and robust two-point finite volume discretization applicable to isotropic linearized elasticity, valid in also in the incompressible Stokes' limit. The discretization is based only on co-located,…

Numerical Analysis · Mathematics 2025-01-22 Jan Martin Nordbotten , Eirik Keilegavlen

Employing the Lax pairs of the noncommutative discrete potential Korteweg--de Vries (KdV) and Hirota's KdV equations, we derive differential--difference equations that are consistent with these systems and serve as their generalised…

Exactly Solvable and Integrable Systems · Physics 2025-07-08 Pavlos Xenitidis

Starting from the Liouville equation, we derive the exact hierarchy of equations satisfied by the reduced distribution functions of the single species point vortex gas in two dimensions. Considering an expansion of the solution in powers of…

Statistical Mechanics · Physics 2009-11-13 P. H. Chavanis

We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…

Numerical Analysis · Mathematics 2017-10-17 Andrea Natale , Colin J. Cotter

In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n, 1) converges to Sn in the C1-topology…

Analysis of PDEs · Mathematics 2011-09-06 De-Xing Kong , Qiang Ru

A general framework for constructing discrete Boltzmann model for non-equilibrium flows based on the Shakhov model is presented. The Hermite polynomial expansion and a set of discrete velocity with isotropy are adopted to solve the kinetic…

Fluid Dynamics · Physics 2019-03-27 Yudong Zhang , Aiguo Xu , Guangcai Zhang , Zhihua Chen , Pei Wang

We use the general exact solution of the Cauchy problem for the compressible Euler vortex equation in unbounded space which was obtained earlier (S.G.Chefranov, Sov. Phys. Dokl., 36, 286, 1991). This solution loses its smoothness in finite…

Fluid Dynamics · Physics 2018-10-31 Sergey G. Chefranov , Artem S. Chefranov