Euler
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Related Articles from SNS
Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
arXiv:2508.21427v2 Announce Type: replace Abstract: The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and the particle density. Kunik et al.\ (2024, https://doi.org/10.1016/j.jcp.2024.113330) proposed genuine multi--dimensional benchmark problems for the ultra--relativistic Euler equations.
Physics-Aware Sparse Learning and Selective Online Adaptation for Euler-Lagrange Robot Dynamics
Announce Type: new Abstract: Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models...
The Semigeostrophic--Euler Limit via Perturbative Monge--Amp\`ere Estimates
arXiv:2601.04797v3 Announce Type: replace-cross Abstract: We study the two-dimensional semigeostrophic system on the flat torus in the small-amplitude regime. We formulate the rescaled dynamics as the Lie--Poisson flow of a renormalized optimal-transport energy and expand this Hamiltonian in \(C^1\). The leading term is the Euler Hamiltonian, while the first correction is an explicit cubic Monge--Amp\`ere functional.
Solitary wave formation in the compressible Euler equations
arXiv:2412.11086v3 Announce Type: replace-cross Abstract: We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength perturbations approximately obey a system of dispersive nonlinear wave equations. Computational experiments demonstrate that solutions of the 1D Euler equations agree well with this dispersive model, with...
Euler-Korteweg vortices: A fluid-mechanical analogue to the Schr\"odinger and Klein-Gordon equations
arXiv:2512.23771v4 Announce Type: replace-cross Abstract: Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schr\"odinger and Klein-Gordon equations.
Adaptive Artificial Time-Delay Control with Barrier Lyapunov Constraints for Euler-Lagrange Robots
Announce Type: new Abstract: This paper addresses the challenge of simultaneously compensating for state-dependent uncertainties and enforcing time-varying state constraints in Euler-Lagrange systems, a common requirement in robotics that remains underserved by existing control designs. A novel adaptive control framework is developed that combines an artificial time-delay-based uncertainty estimation strategy, also known as time-delay estimation, with a barrier Lyapunov function to enforce...
Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics
arXiv:2601.17452v3 Announce Type: replace Abstract: We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposition-based central-upwind (LCDCU), low-dissipation central-upwind (LDCU), and viscous finite volume (VFV) methods, whose higher-order extensions are obtained via the framework of the alternative weighted essentially non-oscillatory (A-WENO) schemes. These methods...
Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques
Announce Type: new Abstract: We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step.
Sharp lower error bounds for strong approximation of SDEs with a drift coefficient of H\"older or Sobolev regularity using a Weierstra{\ss} scale
arXiv:2504.20728v2 Announce Type: replace-cross Abstract: We study strong approximation of solutions of SDEs with bounded $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$. Recently, it was shown in [arXiv:1909.07961v4 (2021)] that for such SDEs the equidistant Euler scheme achieves an $L^p$-error rate of at least $(1+\alpha)/2$, up to an arbitrary small $\varepsilon$, for all $p\geq 1$ and $\alpha\in (0,1]$, in terms of the number of...
Multimodal sampling via Schr\"odinger-F\"ollmer samplers with temperatures
arXiv:2512.23965v2 Announce Type: replace Abstract: Generating samples from complex and high-dimensional distributions is ubiquitous in various scientific fields of statistical physics, Bayesian inference, scientific computing and machine learning. Very recently, Huang et al. Theory, 2025) proposed new Schr\"odinger-F\"ollmer samplers (SFS), based on the Euler discretization of the Schr\"odinger-F\"ollmer diffusion evolving on the unit interval $[0, 1]$. There, a convergence rate of order...