Blowup for the compressible isothermal Euler equations with non-vacuum initial data

Dong, Jianwei

doi:10.1080/00036811.2018.1506103

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…Finally, there is limited work on the mathematical isothermal Euler models which do not consider temperature but instead focus on the equation of state p = ρ. Akin to Sideris' work on nonisentropic Euler [28], Dong [7] proved a blow up result and a finite propagation result when p = ρ. Jenssen-Tsikkou [13] provide a construction of blow-up solutions in the radial setting, and these are shown to be weak solutions to the original p = ρ system.…”

Section: Existence Theories For the Euler Systemmentioning

confidence: 94%

“…Our model admits isothermal solutions in the sense of Dyson and allows the temperature to vary in time. Mathematically, we are deviating slightly from the notion of the isothermal Euler models which do not consider temperature but instead focus on the equation of state p = ρ, see [7,13] for example. However with the equation of state (1.4) p = ρT , and T close to being space independent, our framework shares some mathematical similarities with such previously considered models.…”

Section: Introductionmentioning

confidence: 99%

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Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions

Rickard

2020

Preprint

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Global solutions to the compressible Euler equations with heat transport by convection in the whole space are shown to exist through perturbations of Dyson's isothermal affine solutions [8]. This setting presents new difficulties because of the vacuum at infinity behavior of the density. In particular, the perturbation of isothermal motion introduces a Gaussian function into our stability analysis and a novel finite propagation result is proven to handle potentially unbounded terms arising from the presence of the Gaussian. Crucial stabilization-in-time effects of the background motion are mitigated through the use of this finite propagation result however and a careful use of the heat transport formulation in conjunction with new time weight manipulations are used to establish global existence. The heat transport by convection offers unique physical insights into the model and mathematically, we use a controlled spatial perturbation in the analysis of this feature of our system which leads us to exploit source term estimates as part of our techniques.

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Section: Existence Theories For the Euler Systemmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions

Rickard

2020

Preprint

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“…The isothermal Euler system (1.7) has been studied a lot in different contexts (for example [45,5,23,17,3]). B. Riemann solved the "Riemann problem" for this equation in his memoir to the Royal Academy of Sciences of Göttinger (1860) (see [41]).…”

Section: Riemann Invariantsmentioning

confidence: 99%

WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework

Ferriere

2020

Preprint

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We are interested in a WKB analysis of the Logarithmic Non-Linear Schrödinger Equation with "Riemannlike" variables in an analytic framework in semiclassical regime. We show that the Cauchy problem is locally well posed uniformly in the semiclassical constant and that the semiclassical limit can be performed. In particular, our framework is not only compatible with the Gross-Pitaevskii equation with logarithmic nonlinearity, but also allows initial data (and solutions) which can converge to 0 at infinity.

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“…30 In the operation of the gas pipelines, there are strict upper bounds for the velocities in order to avert noise pollution by pipeline vibrations, which can be generated by the flow. 31,32 For further details concerning the isothermal Euler model, we refer to 33,34 and references therein.…”

Section: Introductionmentioning

confidence: 99%

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Abdelrahman

Alkhidhr

Mohamed

2022

Journal of Low Frequency Noise, Vibration and Active Control

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We consider the isothermal Euler model with non-vacuum initial data. We extract the Riemann invariants of the isothermal Euler model, which admits vital applications. We also design the modified Rusanov (mR) scheme to solve the isothermal Euler model. This scheme consists of two steps, the first step of the scheme depends on a local parameter allowing to control diffusion. The second stage recovers conservation equation. This technique is a straightforward to implement and precise. We compare this scheme with the Rusanov scheme via three numerical examples. This numerical study verifies the efficiency of the mR scheme. Finally, the mR scheme can be used to solve many other models in applied science.

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Blowup for the compressible isothermal Euler equations with non-vacuum initial data

Cited by 6 publications

References 27 publications

Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions

Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions

WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

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