2016
DOI: 10.1002/mma.3885
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Abstract: This paper investigates the smooth solution of 2D Chaplygin gas equations on an asymptotically flat Riemannian manifold. Under the assumption that the initial data are close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of smooth solutions to the Cauchy problem for two-dimensional flow of Chaplygin gases on curved space.

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Cited by 3 publications
(4 citation statements)
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References 22 publications
(23 reference statements)
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“…Kong and Wei in [13] investigated the lifespan of smooth solution to the relativistic membrane equation embedded in de Sitter spacetime when the initial data is sufficiently small and has compact support. Luo and Wei [19] proved the global existence of smooth solutions to 2D isentropic Chaplygin gases without vorticity in curved space when the initial data is small and has compact support. Recently, in order to investigate the influence of the background metric to the stability of the large solution of relativistic membrane equations, Wei [24] studied a class of time-dependent Lorentzian metric and showed that when the decay rate of the derivative of the given metric is larger than 3/2, then a class of time-dependent large solution to the relativistic membrane is globally stable, while, therein, the highest-order energy is still growing with respect to time.…”
Section: Background Materials and Outline Of This Papermentioning
confidence: 99%
“…Kong and Wei in [13] investigated the lifespan of smooth solution to the relativistic membrane equation embedded in de Sitter spacetime when the initial data is sufficiently small and has compact support. Luo and Wei [19] proved the global existence of smooth solutions to 2D isentropic Chaplygin gases without vorticity in curved space when the initial data is small and has compact support. Recently, in order to investigate the influence of the background metric to the stability of the large solution of relativistic membrane equations, Wei [24] studied a class of time-dependent Lorentzian metric and showed that when the decay rate of the derivative of the given metric is larger than 3/2, then a class of time-dependent large solution to the relativistic membrane is globally stable, while, therein, the highest-order energy is still growing with respect to time.…”
Section: Background Materials and Outline Of This Papermentioning
confidence: 99%
“…Kong and Wei obtained the life span of the solution to in de Sitter space‐time. Inspired by the relationship between relativistic membrane equations and Chaplygin gases, Luo and Wei proved the global existence of smooth solutions to 2D isentropic Chaplygin gases without vorticity in curved space when the initial data is small and has compact support. It is necessary to emphasize that the equation studied in Luo and Wei is a simplified model of the problem considered here.…”
Section: Introductionmentioning
confidence: 99%
“…Inspired by the relationship between relativistic membrane equations and Chaplygin gases, Luo and Wei proved the global existence of smooth solutions to 2D isentropic Chaplygin gases without vorticity in curved space when the initial data is small and has compact support. It is necessary to emphasize that the equation studied in Luo and Wei is a simplified model of the problem considered here. Different from our earlier work, we consider the stability of a given nontrivial large solution, which is more difficult than the stability of the trivial solution.…”
Section: Introductionmentioning
confidence: 99%
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