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Double Asymptotic Expansion of the Resolving Operator of the Cauchy Problem for the Linearized System of Gas Dynamics

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Abstract

A double asymptotic expansion (with respect to smoothness and low viscosity) of the resolving operator of the Cauchy problem for the linearized system of gas dynamics is obtained. Estimates for the summands and the remainder are derived in the Sobolev scale. Hydrodynamic and acoustic modes are explicitly described.

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REFERENCES

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ACKNOWLEDGMENTS

This work was supported by the Russian Science Foundation, grant no. 16-11-10282.

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Authors and Affiliations

  1. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    A. I. Allilueva &  A. I. Shafarevich

  2. Moscow Institute of Physics and Technology (State University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    A. I. Allilueva &  A. I. Shafarevich

  3. National Research Center “Kurchatov Institute”, 123182, Moscow, Russia

    A. I. Allilueva &  A. I. Shafarevich

  4. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    A. I. Shafarevich

Authors
  1. A. I. Allilueva
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  2. A. I. Shafarevich
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Correspondence to A. I. Shafarevich.

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Translated by I. Ruzanova

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Allilueva, A.I., Shafarevich, A.I. Double Asymptotic Expansion of the Resolving Operator of the Cauchy Problem for the Linearized System of Gas Dynamics. Dokl. Math. 99, 16–19 (2019). https://doi.org/10.1134/S106456241901006X

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  • DOI: https://doi.org/10.1134/S106456241901006X

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