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The fluid structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian-Eulerian hybrid flow solver. In this hybrid combination, separate grids of limited width are defined around every…

Fluid Dynamics · Physics 2022-07-20 George Papadakis , Vasilis A. Riziotis , Spyros G. Voutsinas

The Euler equations on a three-dimensional periodic domain have a family of shear flow steady states. We show that the linearised system around these steady states decomposes into subsystems equivalent to the linearisation of shear flows in…

Dynamical Systems · Mathematics 2020-09-07 Holger R. Dullin , Joachim Worthington

In this article we construct a smooth Euler flow supported in a neighborhood of a helix. It may be considered a generalization of a similar solution found by the author for a circle.

Differential Geometry · Mathematics 2019-06-19 A. V. Gavrilov

This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the…

Analysis of PDEs · Mathematics 2007-05-23 Steve Shkoller

We have explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of…

Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…

Fluid Dynamics · Physics 2017-03-30 Che Sun

We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler-Poisson system in a cylinder supplemented with non small boundary data. A special Helmholtz decomposition of the…

Analysis of PDEs · Mathematics 2016-05-09 Myoungjean Bae , Shangkun Weng

This paper concerns the existence of transonic shocks for steady exothermically reacting Euler flows in an almost flat nozzle with the small rate of the exothermic reaction. One of the key points is to quantitatively determine the position…

Analysis of PDEs · Mathematics 2023-01-02 Beixiang Fang , Piye Sun , Qin Zhao

This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…

We review and apply the continuous symmetry approach to find the solution of the 3D Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to…

Fluid Dynamics · Physics 2022-01-25 Miguel D. Bustamante

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…

Analysis of PDEs · Mathematics 2026-04-17 Gunther Uhlmann , Yuchao Yi , Jian Zhai

Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler…

Fluid Dynamics · Physics 2013-09-10 Liang Sun

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter…

Analysis of PDEs · Mathematics 2022-10-10 Yan Guo , Benoit Pausader , Klaus Widmayer

In this paper, we are concerned with the existence of transonic shock solutions for two-dimensional (2-d) steady Euler flows of polytropic gases with the vertical gravity in a horizontal nozzle under a pressure condition imposed at the exit…

Analysis of PDEs · Mathematics 2025-04-08 Beixiang Fang , Xin Gao , Wei Xiang , Qin Zhao

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

We study closed, embedded hypersurfaces in Euclidean space evolving by fully nonlinear curvature flows, whose speed is given by a symmetric, monotone increasing, $1$-homogeneous, positive underlying speed function $F$ composed with a…

Differential Geometry · Mathematics 2025-09-29 Weimin Sheng , Ye Zhu

We investigate two dimensional steady Euler-Poisson system which describe the motion of compressible self-gravitating flows. The unique existence and stability of subsonic flows in a duct of finite length are obtained when prescribing the…

Analysis of PDEs · Mathematics 2014-06-18 Myoungjean Bae , Ben Duan , Chunjing Xie

We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…

Analysis of PDEs · Mathematics 2023-01-19 Guodong Wang , Bijun Zuo

We consider the Cauchy problems of a non-strictly hyperbolic system which describes the compressible Euler fluid with exothermic reaction. In this paper a Lyapunov-type functional is constructed for balance laws. By analysis of the flow…

Dynamical Systems · Mathematics 2018-01-30 Kai Hu

In this paper we prove existence, uniqueness and regularity of certain perturbed (subsonic--supersonic) transonic potential flows in a two-dimensional Riemannian manifold with "convergent-divergent" metric, which is an approximate model of…

Analysis of PDEs · Mathematics 2011-02-19 Hairong Yuan , Yue He