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Related papers: Mach limits in analytic spaces

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We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical…

General Relativity and Quantum Cosmology · Physics 2017-06-15 Moritz Reintjes

We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are…

Analysis of PDEs · Mathematics 2010-11-04 Bin Cheng

In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small…

Analysis of PDEs · Mathematics 2022-07-07 Xiang Bai , Qianyun Miao , Changhui Tan , Liutang Xue

Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed and an explanation is provided by comparing a…

Fluid Dynamics · Physics 2024-02-06 Carlos Lozano , Jorge Ponsin

We study in this paper the low Mach number limit for the 2d isentropic Euler system with ill-prepared initial data belonging to the critical Besov space $B_{2,1}^2$. By combining Strichartz estimates with the special structure of the…

Analysis of PDEs · Mathematics 2012-03-20 Taoufik Hmidi , Samira Sulaiman

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation…

Analysis of PDEs · Mathematics 2016-11-24 Feng Cheng , Wei-Xi Li , Chao-Jiang Xu

Two compressible immiscible fluids in 1D and in the isentropic approximation are considered. The first fluid is surrounded and in contact with the second one. As the Mach number of the first fluid vanishes, we prove the rigorous convergence…

Analysis of PDEs · Mathematics 2015-09-08 Rinaldo M. Colombo , Graziano Guerra

We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken…

Analysis of PDEs · Mathematics 2019-04-09 Aifang Qu , Hairong Yuan , Qin Zhao

After reformulate the incompressible Euler-$\alpha$ equations in 3D smooth domain with Drichlet data, we obtain the unique classical solutions to Euler-$\alpha$ equations exist in uniform time interval independent of $\alpha$. We also show…

Analysis of PDEs · Mathematics 2016-04-19 Aibin Zang

We consider a singular limit problem for the complete compressible Euler system in the low Mach and strong stratification regime. We identify the limit problem - the anelastic Euler system - in the case of well prepared initial data. The…

Analysis of PDEs · Mathematics 2018-05-18 Gabriele Bruell , Eduard Feireisl

An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…

Atmospheric and Oceanic Physics · Physics 2016-12-20 Juan Simarro , Petra Smolikova , Jozef Vivoda

We consider the incompressible Euler equations on ${\mathbb R}^d$, where $d \in \{ 2,3 \}$. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a…

Analysis of PDEs · Mathematics 2016-12-21 Peter Constantin , Igor Kukavica , Vlad Vicol

We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…

Numerical Analysis · Mathematics 2026-03-31 Megala Anandan , K. R. Arun , Amogh Krishnamurthy , Mária Lukáčová-Medvid'ová

We prove a rigorous convergence result for the compressible to incompressible limit of weak entropy solutions to the isothermal 1D Euler equations.

Analysis of PDEs · Mathematics 2013-08-20 Rinaldo M. Colombo , Graziano Guerra , Veronika Schleper

This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data…

Analysis of PDEs · Mathematics 2020-08-26 Xin Liu , Edriss S. Titi

We obtain a uniform linear bound for the Chevalley function at a point in the source of an analytic mapping that is regular in the sense of Gabrielov. There is a version of Chevalley's lemma also along a fibre, or at a point of the image of…

Algebraic Geometry · Mathematics 2007-05-23 J. Adamus , E. Bierstone , P. D. Milman

We study the low Mach number limit of the compressible Navier-Stokes equations on the torus. For large initial data with critical regularity, we prove that solutions to the compressible Navier-Stokes system exist as long as the…

Analysis of PDEs · Mathematics 2026-03-03 Sai Li

In this paper, we study the low Mach number limit of the full compressible Navier-Stokes equations with revised Maxwell law. By applying the uniform estimation of the error system, we prove that the solutions of the full compressible…

Analysis of PDEs · Mathematics 2020-11-19 Zhao Wang , Yuxi Hu

In this paper we establish the incompressible limit for the compressible free-boundary Euler equations with surface tension in the case of a liquid. Compared to the case without surface tension treated recently, the presence of surface…

Analysis of PDEs · Mathematics 2020-05-14 Marcelo M. Disconzi , Chenyun Luo

We are concerned with global existence of regular solutions to full compressible Navier-Stokes equations and their asymptotic behavior when the Mach number is sufficiently small. We establish global existence in critical Besov spaces for…

Analysis of PDEs · Mathematics 2026-03-03 Sai Li