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Exact Local Controllability of a Two-Dimensional Viscous Gas Flow

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Abstract

In a two-dimensional bounded domain \(\Omega \), we consider the system of Navier–Stokes equations describing the flow of a viscous compressible gas with no allowance for heat exchange with the ambient medium under small variations of density in the equations of motion. We prove the existence of a solution to the problem of exact local controllability of this system by an external force supported in an arbitrary fixed subdomain \(\omega \subset \Omega \).

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 20-01-00113.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far East Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia

    E. V. Amosova

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  1. E. V. Amosova
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Correspondence to E. V. Amosova.

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Translated by V. Potapchouck

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Amosova, E.V. Exact Local Controllability of a Two-Dimensional Viscous Gas Flow. Diff Equat 56, 1416–1439 (2020). https://doi.org/10.1134/S0012266120011004X

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