Existence and regularity of solutions of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow with general equation of state

Barthwal, Rahul; Sekhar, T. Raja

doi:10.1016/j.jmaa.2023.127022

Cited by 4 publications

(4 citation statements)

References 44 publications

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“…where 𝑐(𝜏) = √ −𝜏 2 𝑝 ′ (𝜏) is the speed of sound. It is straightforward to see that the eigenvalues of the system (7) are 2 with corresponding left eigenvectors 𝑙 ± = (1, 𝜆 ∓ ). The expression of these eigenvalues shows that the system ( 7) is a mixed-type system and changes its behavior from hyperbolic to elliptic across the sonic boundary and depends on the choice of pseudo-…”

Section: System In (𝝃 𝜼) Planementioning

confidence: 99%

“…We call these characteristic curves positive (𝐶 + ) and negative (𝐶 − ) characteristics, respectively. Moreover, we obtain the characteristic equations by multiplying 𝑙± to the system (7) as…”

Section: System In (𝝃 𝜼) Planementioning

confidence: 99%

“…In recent years, a lot of significant work has been done for the 2-D compressible Euler system as well as numerous other related models for a variety of initial and boundary value problems; see, namely, Refs. [5][6][7][8][9][10][11][12][13][14][15][16]. In particular, for gas expansion problems through a sharp corner or wedge, we refer the reader to Refs.…”

Section: Introductionmentioning

confidence: 99%

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Existence of solutions to gas expansion problem through a sharp corner for 2‐D Euler equations with general equation of state

Barthwal

Sekhar

2023

Stud Appl Math

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In this article, we study the gas expansion problem by turning a sharp corner into a vacuum for the two‐dimensional (2‐D) pseudosteady compressible Euler equations with a convex equation of state. This problem can be considered as the interaction of a centered simple wave with a planar rarefaction wave. To obtain the global existence of a solution up to the vacuum boundary of the corresponding 2‐D Riemann problem, we consider several Goursat‐type boundary value problems for 2‐D self‐similar Euler equations and use the ideas of characteristic decomposition and bootstrap method. Further, we formulate 2‐D‐modified shallow water equations newly and solve a dam‐break‐type problem for them as an application of this work. Moreover, we also recover the results from the available literature for certain equations of states that provide a check that the results obtained in this article are actually correct.

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Section: System In (𝝃 𝜼) Planementioning

confidence: 99%

Section: System In (𝝃 𝜼) Planementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence of solutions to gas expansion problem through a sharp corner for 2‐D Euler equations with general equation of state

Barthwal

Sekhar

2023

Stud Appl Math

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“…The existence and regularity of sonic-supersonic patch arised in transonic flow problem for general equation of state has been discussed by R. Barthwal and T. R. Sekhar (see Ref. 37).…”

Section: Introductionmentioning

confidence: 99%

Degenerate Cauchy–Goursat problem for 2‐D steady isentropic Euler system with van der Waals gas

Srivastava,

Zafar

2023

Stud Appl Math

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This study concerns with the existence–uniqueness of local classical sonic‐supersonic solution to a degenerate Cauchy–Goursat problem that arises in transonic phenomena. The flow is governed by 2‐D steady isentropic Euler system with a polytropic van der Waals gas. The idea of characteristic decomposition has been used to convert the Euler system into a new system involving the angle variables . To overcome the parabolic degeneracy caused at the sonic curve, the partial hodograph transformation and a variety of dependent–independent variables have been introduced to transform the nonlinear system into a linear one with explicit singularity–regularity structure. The uniform convergence of the sequences has been discussed by employing the mathematical induction. Eventually, the inversion of the solution from partial hodograph plane to the original plane has been established.

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On a degenerate boundary value problem to relativistic magnetohydrodynamics with a general pressure law

Barthwal,

Sekhar

2024

Z. Angew. Math. Phys.

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Existence and regularity of solutions of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow with general equation of state

Cited by 4 publications

References 44 publications

Existence of solutions to gas expansion problem through a sharp corner for 2‐D Euler equations with general equation of state

Existence of solutions to gas expansion problem through a sharp corner for 2‐D Euler equations with general equation of state

Degenerate Cauchy–Goursat problem for 2‐D steady isentropic Euler system with van der Waals gas

On a degenerate boundary value problem to relativistic magnetohydrodynamics with a general pressure law

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