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Multi-dimensional Wave Propagation Over a Burgers Shock Profile

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Abstract

We study the stability of viscous shock profiles under multi-dimensional perturbation in order to understand the propagation ofmulti-dimensional dispersionwaves over the compressive shock profile. Our analysis is based on the new algorithm of explicitly constructing the Green’s function for the system linearized around the shock profile. We first construct Green’s function for the system linearized around the inviscid profile by matching the two half space problems. The Green’s function around the shock profile is then constructed by iterations. Our approach is of a general nature. We carry out the approach for a simple model possessing the Burgers shocks and wave structure similar to acoustic cones in multi-dimensional gas flows. The approach exhibits a rich phenomenon of wave propagation along and dispersing away from the shock profile.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Taipei, China

    Tai-** Liu

  2. Department of Mathematics, Stanford University, Stanford, USA

    Tai-** Liu

  3. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Shih-Hsien Yu

Authors
  1. Tai-** Liu
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  2. Shih-Hsien Yu
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Correspondence to Tai-** Liu.

Additional information

Communicated by C. Dafermos

Shih-Hsien Yu: The research of the first author is supported by Institute of Mathematics, Academia Sinica, MOST Grant 106-2115-M-001-005, and Simons Fundation Grant. The research of the second author is supported by Singapore MOE TIER I R-146-000-221-112 and the National University of Singapore

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Liu, TP., Yu, SH. Multi-dimensional Wave Propagation Over a Burgers Shock Profile. Arch Rational Mech Anal 229, 231–337 (2018). https://doi.org/10.1007/s00205-018-1217-5

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  • DOI: https://doi.org/10.1007/s00205-018-1217-5

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