Optimal Control for Linearized Non-Isentropic Compressible Navier–Stokes Equations

Di Pan; Wenshuo Du; Wei Sun; Runmei Du

doi:10.3390/math14030515

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Article

31 January 2026

Optimal Control for Linearized Non-Isentropic Compressible Navier–Stokes Equations

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School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China

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Mathematics2026, 14(3), 515;https://doi.org/10.3390/math14030515
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This article belongs to the Section E2: Control Theory and Mechanics

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Abstract

This paper investigates the optimal control problem for the non-isentropic compressible Navier–Stokes equations linearized around a constant steady state. First, we establish estimates for the solution of the state equation. Then, we prove the existence and uniqueness of the optimal control, derive the necessary optimality conditions, and obtain an explicit characterization of the control via the optimality system. Finally, we present a numerical experiment to compute the control using the derived formula.

Keywords:

optimal control; Navier–Stokes equations; non-isentropic compressible fluids

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