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We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

Numerical Analysis · Mathematics 2024-06-06 Anders Melander , Max E. Bitsch , Dong Chen , Allan P. Engsig-Karup

In this paper, we introduce and analyze a space-time $p$-adaptive discontinuous Galerkin method for nonlinear acoustics. We first present the underlying mathematical model, which is based on a recently derived formulation involving, in…

Numerical Analysis · Mathematics 2026-02-16 Daniele Corallo , Pascal Lehner , Christian Wieners

We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wise mass conservation, energy stability, and pressure…

Numerical Analysis · Mathematics 2023-07-07 Keegan L. A. Kirk , Tamás L. Horváth , Sander Rhebergen

We consider a nonlinear fourth order in space partial differential equation arising in the context of the modeling of nonlinear acoustic wave propagation in thermally relaxing viscous fluids. We use the theory of operator semigroups in…

Analysis of PDEs · Mathematics 2015-09-25 Rainer Brunnhuber , Barbara Kaltenbacher

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

Analysis of PDEs · Mathematics 2025-09-23 Zihua Guo , Zihao Song , Minghua Yang

The pressureless Euler-Navier-Stokes system can be obtained formally from the Vlasov-Navier-Stokes system, under the assumption that the distribution function describing the density of particles is monokinetic. Its study has been the…

Analysis of PDEs · Mathematics 2026-02-09 Raphaël Danchin

We establish a solution theory for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity can be solved…

Probability · Mathematics 2026-03-30 Benjamin Gess , Max Sauerbrey , Zhengyan Wu

The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…

Numerical Analysis · Mathematics 2025-10-20 Mathias Anselmann , Markus Bause

In the present paper we study slow-fast systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of…

Probability · Mathematics 2025-07-28 Arnaud Debussche , Umberto Pappalettera

First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with $L^2$ initial data in convex polygonal domains, without extra regularity…

Numerical Analysis · Mathematics 2021-01-19 Buyang Li , Shu Ma , Yuki Ueda

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

Numerical Analysis · Mathematics 2023-01-16 Erik Burman , Deepika Garg , Janosch Preuss

In this paper we describe a method to derive solutions of the incompressible Navier- Stokes system of equations for non-stationary initial value problems in $\mathbb{R}^n$. We show that for a given smooth solenoidal initial velocity vector…

Analysis of PDEs · Mathematics 2016-03-29 R. K. Michael Thambynayagam

This paper is concerned with a kineitc-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier-Stokes equations and the Vlasov-Fokker-Planck equations that model dispersed…

Analysis of PDEs · Mathematics 2022-04-25 Shi Jin , Yiwen Lin

This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative…

Numerical Analysis · Mathematics 2025-10-10 Xiaobing Feng , Liet Vo

We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…

Analysis of PDEs · Mathematics 2025-04-15 D. Breit , E. Feireisl , M. Hofmanova , P. B. Mucha

We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the space--time formulation of the Navier--Stokes…

Numerical Analysis · Mathematics 2023-07-06 Tamas L. Horvath , Sander Rhebergen

A novel reduced-order model for nonlinear flows is presented. The model arises from a resolvent decomposition in which the nonlinear advection terms of the Navier-Stokes equation are considered as the input to a linear system in Fourier…

Fluid Dynamics · Physics 2016-06-16 F Gómez , HM Blackburn , M Rudman , AS Sharma , BJ McKeon

We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier--Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only…

Analysis of PDEs · Mathematics 2024-07-15 Dan Crisan , Prince Romeo Mensah

In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler--Navier--Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two…

Analysis of PDEs · Mathematics 2023-07-10 Young-Pil Choi , Jinwook Jung , Junha Kim

In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…

Numerical Analysis · Mathematics 2019-02-08 Giovanni Stabile , Gianluigi Rozza