Existence and asymptotic behavior of C1 solutions to the multi-dimensional compressible Euler equations with damping

Fang, Daoyuan; Xu, Jiang

doi:10.1016/j.na.2007.11.049

Cited by 57 publications

(49 citation statements)

References 13 publications

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“…Since n has a positive lower bound, there exist two positive constants a and b such that γ−1 2 m 0 + ψ ∈ [2a, b] and |u 0 | ≤ b for all x. From [4], we can denote by [0, T ) the maximal time interval where the symmetric hyperbolic system (2.1) and (2.2) has a unique B σ+δ 2,2 -solution (m , u ) with values in…”

Section: Resultsmentioning

confidence: 99%

“…By multiplying (4.2) by Δ q E m , Δ q E u respectively and integrating them over R d , we can achieve (4.3) without extra troubles, also see [4] for similar details.…”

Section: Multi-dimensional Isentropic Euler Equations 395mentioning

confidence: 91%

“…In additional, many efforts on the global existence and asymptotic stability of smooth solutions to (1.1) and generally quasi-linear hyperbolic system should be mentioned, e.g., see [4,5,12,18] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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Strong relaxation limit of multi-dimensional isentropic Euler equations

2009

Z. Angew. Math. Phys.

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This paper is devoted to study the strong relaxation limit of multi-dimensional isentropic Euler equations with relaxation. Motivated by the Maxwell iteration, we generalize the analysis of Yong (SIAM J Appl Math 64: [1737][1738][1739][1740][1741][1742][1743][1744][1745][1746][1747][1748] 2004) and show that, as the relaxation time tends to zero, the density of a certain scaled isentropic Euler equations with relaxation strongly converges towards the smooth solution to the porous medium equation in the framework of Besov spaces with relatively lower regularity. The main analysis tool used is the Littlewood-Paley decomposition. (2000). Primary 35L45; Secondary 76N15, 35B25, 35L65. Mathematics Subject Classification

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Section: Resultsmentioning

confidence: 99%

“…By multiplying (4.2) by Δ q E m , Δ q E u respectively and integrating them over R d , we can achieve (4.3) without extra troubles, also see [4] for similar details.…”

Section: Multi-dimensional Isentropic Euler Equations 395mentioning

confidence: 91%

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Strong relaxation limit of multi-dimensional isentropic Euler equations

2009

Z. Angew. Math. Phys.

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“…Thanks to Lemma 2.4 on continuity of composition, it suffices to prove Theorem 1.1 for the system (9)- (10). To this end, we definẽ…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

“…This principle is based on Iftimie's local existence theory of smooth solutions to generally symmetric hyperbolic systems [9]. Actually, the local existence for the Euler equations and Euler-Poisson equations in the same critical spaces was independently obtained in [10,11]. These results dealt with some concrete contents, e.g.…”

Section: Introductionmentioning

confidence: 99%

A note on incompressible limit for compressible Euler equations

Xu¹,

Yong²

2011

Math. Meth. Appl. Sci.

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Communicated by X. WangThis paper presents a simple justification of the classical low Mach number limit in critical Besov spaces for compressible Euler equations with prepared initial data. As the first step of this justification, we formulate a continuation principle for general hyperbolic singular limit problems in the framework of critical Besov spaces. With this principle, it is also shown that, for the Mach number sufficiently small, the smooth compressible flows exist on the (finite) time interval where the incompressible Euler equations have smooth solutions, and the definite convergence orders are obtained.

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