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In this paper, we consider numerical approximations for solving the micropolar Navier-Stokes (MNS) equations, that couples the Navier-Stokes equations and the angular momentum equation together. By combining the scalar auxiliary variable…

Numerical Analysis · Mathematics 2022-10-07 Xiaodi Zhang , Xiaonian Long

We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is…

Analysis of PDEs · Mathematics 2020-10-23 Dan Crisan , Oana Lang

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding…

Analysis of PDEs · Mathematics 2021-02-04 Piotr Minakowski , Piotr B. Mucha , Jan Peszek , Ewelina Zatorska

The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to…

Numerical Analysis · Mathematics 2024-10-15 Eike Hermann Müller

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…

Analysis of PDEs · Mathematics 2025-08-27 David I. Ketcheson , Giovanni Russo

We consider a special class of infinite energy solutions to the inviscid incompressible porous medium equations (IPM), introduced in Castro-C\'ordoba-Gancedo-Orive [9]. The (IPM) equations then reduce to a one-dimensional nonlocal nonlinear…

Analysis of PDEs · Mathematics 2025-07-24 Charles Collot , Christophe Prange , Jin Tan

In this paper we study cosmological solutions to the Einstein--Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly…

Analysis of PDEs · Mathematics 2024-07-25 David Fajman , Maximilian Ofner , Todd A. Oliynyk , Zoe Wyatt

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The…

Analysis of PDEs · Mathematics 2020-09-24 Alessandro Morando , Paola Trebeschi , Tao Wang

We consider the two dimensional unsteady Prandtl system. For a special class of outer Euler flows and solutions of the Prandtl system, the trace of the tangential derivative of the tangential velocity along the transversal axis solves a…

Analysis of PDEs · Mathematics 2022-04-08 Charles Collot , Tej-Eddine Ghoul , Slim Ibrahim , Nader Masmoudi

Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of singularly perturbed Klein-Gordon-Maxwell systems and Schroedinger-Maxwell systems on M, with a subcritical nonlinearity. We prove that…

Mathematical Physics · Physics 2013-02-20 Marco Ghimenti , Anna Maria Micheletti , Angela Pistoia

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three…

Fluid Dynamics · Physics 2022-03-02 Saikumar R. Yeddula , Juan Guzmán-Iñigo , Aimee S. Morgans

This document presents a quantum-inspired solver for 2D Euler equations, accepted at the final phase of the Airbus-BWM Group Quantum Computing Challenge (ABQCC) 2024. We tackle the case study of Quantum Solvers for Predictive Aeroacoustic…

For the one-stage third-order gas-kinetic scheme (GKS), success applications have been achieved for the three-dimensional compressible flow computations [33]. The high-order accuracy of the scheme is obtained directly by integrating a…

Numerical Analysis · Mathematics 2019-02-20 Liang Pan , Kun Xu

We consider the (repulsive) Euler-Poisson system for the electrons in two dimensions and prove that small smooth perturbations of a constant background exist for all time and remain smooth (never develop shocks). This extends to 2D the work…

Analysis of PDEs · Mathematics 2011-10-05 Alexandru D. Ionescu , Benoit Pausader

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…

Analysis of PDEs · Mathematics 2013-05-07 Demetrios Christodoulou , Shuang Miao

Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…

Fluid Dynamics · Physics 2025-10-17 Xi Deng , Bin Xie , Omar K. Matar , Pierre Boivin

In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on…

Numerical Analysis · Mathematics 2021-04-12 M. Siebenborn , V. Schulz , S. Schmidt

We present a high-order implicit-explicit discontinuous Galerkin (IMEX-DG) solver for the compressible Euler equations to account for rotational effects within a fully compressible atmospheric framework. Time integration follows a…

Numerical Analysis · Mathematics 2026-05-29 Letizia Bottani , Tommaso Benacchio , Giuseppe Orlando , Luca Bonaventura , Allan Peter Engsig-Karup

The multidimensional gas-kinetic scheme for the Navier-Stokes equations under gravitational fields [J. Comput. Phys. 226 (2007) 2003-2027] is extended to resistive magnetic flows. The non-magnetic part of the magnetohydrodynamics equations…

Instrumentation and Methods for Astrophysics · Physics 2010-10-19 Chun-Lin Tian

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…

Numerical Analysis · Mathematics 2026-01-28 Shaoshuai Chu , Michael Herty , Alexander Kurganov , Maria Lukacova-Medvidova , Changsheng Yu