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Abstract:
Considering the space-periodic perturbations, we prove the time-asymptotic stability of the composite wave of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations in this paper. Perturbations of this kind oscillate in the far field and are not integrable. The key is to construct a suitable ansatz carrying the same oscillation as that of the initial data, but due to the degeneration of contact discontinuity, the construction is more subtle. A novel method for constructing robust ansatzes is presented. It allows the same weight function to be used on different variables and wave patterns while maintaining control over the errors. As a result, it is possible to apply this construction to contact discontinuities and composite waves. Lastly, we demonstrate that the Cauchy problem admits a unique global-in-time solution and the composite wave remains stable under space-periodic perturbations through the energy method. (c) 2022 Elsevier Inc. All rights reserved.
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Source :
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN: 0022-0396
Year: 2023
Volume: 346
Page: 254-276
2 . 4 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:9
Cited Count:
WoS CC Cited Count: 4
SCOPUS Cited Count: 4
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 9
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