Perturbational blowup solutions to the compressible 1-dimensional Euler equations

Yuen, Manwai

doi:10.1016/j.physleta.2011.09.001

Cited by 15 publications

(16 citation statements)

References 10 publications

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“…For non-rotational flows, Makino first obtained the radial symmetry solutions for the Euler equations (1) in R N in 1993 [9]. A number of special solutions for these equations [6], [7], [12], [13], and [14] were subsequently obtained. For rotational flows, Zhang and Zheng [15] constructed explicitly rotational solutions for the Euler equations with γ = 2 in 1997:…”

Section: Mwyuenmentioning

confidence: 99%

Vortical and self-similar flows of 2D compressible Euler equations

Yuen

2014

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tThis paper presents the vortical and self-similar solutions for 2D compressible Euler equations using the separation method. These solutions complement Makino's solutions in radial symmetry without rotation. The rotational solutions provide new information that furthers our understanding of ocean vortices and reference examples for numerical methods. In addition, the corresponding blowup, time-periodic or global existence conditions are classified through an analysis of the new Emden equation. A conjecture regarding rotational solutions in 3D is also made.

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Section: Mwyuenmentioning

confidence: 99%

Vortical and self-similar flows of 2D compressible Euler equations

Yuen

2014

Communications in Nonlinear Science and Numerical Simulation

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“…Different from the works mentioned above, here we plan to study the exact self-similar blowup solutions of WBK equations via the perturbational method [14,15]. Recently, such type solutions have been studied extensively and intensively (see references e.g.…”

Section: Introductionmentioning

confidence: 99%

Exact self-similar perturbational solutions of Whitham-Broer-Kaup equations

Cheung¹

2014

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In this paper, by employing the perturbational method, we obtain a class of exact self-similar solutions of the Whitham-Broer-Kaup equations. These solutions are of polynomials-type whose forms, remarkably, coincident with that given by Yuen for the other physical models, such as the compressible Euler or Navier-Stokes equations, two-component Camassa-Holm equations and viscoelastic Burgers equations.

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“…After that there are some other ways to construct some particular solutions [3] and [8] for these systems.…”

Section: Introductionmentioning

confidence: 99%

Self-similar solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in RN

Yuen

2012

Communications in Nonlinear Science and Numerical Simulation

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Based on Makino's solutions with radially symmetry, we extend the corresponding ones with elliptic symmetry for the compressible Euler and Navier-Stokes equations in R N (N ≥ 2).By the separation method, we reduce the Euler and Navier-Stokes equations into 1 + N differential functional equations. In detail, the velocity is constructed by the novel Emden dynamical system:with arbitrary constants ξ, ai0 and ai1. Some blowup phenomena or global existences of the solutions obtained could be shown.

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Perturbational blowup solutions to the compressible 1-dimensional Euler equations

Abstract: We study the construction of analytical non-radially solutions for the 1-dimensional compressible adiabatic Euler equations in this article. We could design the perturbational method to construct a new class of analytical solutions. In details, we perturb the linear velocity:

Cited by 15 publications

References 10 publications

Vortical and self-similar flows of 2D compressible Euler equations

Vortical and self-similar flows of 2D compressible Euler equations

Exact self-similar perturbational solutions of Whitham-Broer-Kaup equations

Self-similar solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in RN

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