2007
DOI: 10.1512/iumj.2007.56.3063
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Dependence of entropy solutions in the large for the Euler equations on nonlinear flux functions

Abstract: Abstract. We study the dependence of entropy solutions in the large for hyperbolic systems of conservation laws whose flux functions depend on a parameter vector µ. We first formulate an effective approach for establishing the L 1 -estimate pointwise in time between entropy solutions for µ = 0 and µ = 0, respectively, with respect to the flux parameter vector µ. Then we employ this approach and successfully establish the L 1 -estimate between entropy solutions in the large for several important nonlinear physi… Show more

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Cited by 14 publications
(11 citation statements)
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“…Due to the high complexity of the system itself, current efforts have been made mainly to the corresponding reduced 2 × 2 systems, involving either the conserved equations of baryon numbers and momentum or the conserved equations of momentum and energy(see [2][3][4][5]7,8,[10][11][12][13][14][15]19,[21][22][23][24][25]27,35,36] etc., and the references cited therein).…”
Section: Introductionmentioning
confidence: 99%
“…Due to the high complexity of the system itself, current efforts have been made mainly to the corresponding reduced 2 × 2 systems, involving either the conserved equations of baryon numbers and momentum or the conserved equations of momentum and energy(see [2][3][4][5]7,8,[10][11][12][13][14][15]19,[21][22][23][24][25]27,35,36] etc., and the references cited therein).…”
Section: Introductionmentioning
confidence: 99%
“…The conditions on the initial data are the same as obtained in [21] and [17]. In [7,8] front tracking is used to study systems of conservation laws whose flux functions depend on a parameter vector, µ, similar to those in [25]. An approach for establishing L 1 -estimate pointwise in time between entropy solutions for µ = 0 and µ = 0 is given.…”
Section: Introductionmentioning
confidence: 99%
“…An approach for establishing L 1 -estimate pointwise in time between entropy solutions for µ = 0 and µ = 0 is given. In particular, letting µ = γ − 1, the L 1 -estimate between entropy solutions in the large for the isentropic Euler equations and the isothermal Euler equations is established in [7] and between entropy solutions in the large for the the Euler equations and the isothermal Euler equations in [8].…”
Section: Introductionmentioning
confidence: 99%
“…Much progress has been made to the mathematical theory of relativistic fluid dynamics, yet mainly for one-dimensional system or spherically symmetric three-dimensional system (see [2][3][4][5][6][7]9,11,[15][16][17][18][19][20]22,27,28,34,37,44,45] and references cited therein). For multi-dimensional cases, local existence results of smooth solutions were obtained in [24,25], the singularity formation of smooth solutions was studied in [12,26,30].…”
Section: Introductionmentioning
confidence: 99%