Solving the Einstein Equations by Lipschitz Continuous Metrics: Shock Waves in General Relativity

Groah, Jeff; Smoller, Joel; Temple, Blake

doi:10.1016/s1874-5792(03)80013-7

Cited by 1 publication

(1 citation statement)

References 39 publications

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“…where S(r, t, U) is called the contraction matrix which depending on U (as well as f, g). This construction of the generalised Riemann solver is different from the other operator splitting methods [1,8,12] and the fractional step scheme [18]. For the stability of the generalised Glimm scheme, the authors in [4,5,9,10,18] assume that the gas velocity is always positive.…”

Section: Introductionmentioning

confidence: 99%

Global transonic solutions of hot-Jupiter model for exoplanetary atmosphere

Chou,

Huang

2024

Nonlinearity

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In this paper, we make modifications to the original hot-Jupiter model, which addresses the problem of hydrodynamic escape for the planetary atmosphere. The model involves the Euler equation with gravity, tidal effect, and heat. We employ the generalised Glimm technique to prove the presence of transonic solutions to the problem. By adjusting the dilation of the characteristic fields, we enhance the accuracy of the Glimm–Goodman wave interaction estimates. This allows us to establish a more general admissible condition for stabilizing the generalised Glimm scheme. Additionally, we derive the exact relationship between the lower bound of the gas velocity in the subsonic state and the adiabatic constant of the gas. Under certain constraints on the transonic initial and boundary data, the limit of the approximation solutions represents an entropy transonic solution with bounded variations. Furthermore, we are able to determine the feasible hydrodynamical region directly from the equation itself, without the need for any additional state equation.

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