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Viscosity Solutions of Dynamic-Programming Equations for the Optimal Control of the Two-Dimensional Navier-Stokes Equations

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Abstract

In this paper we study the infinite-dimensional Hamilton-Jacobi equation associated with the optimal feedback control of viscous hydrodynamics. We resolve the global unique solvability problem of this equation by showing that the value function is the unique viscosity solution.

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Authors and Affiliations

  1. Dipartimento di Matematica per le Decisioni¶Economiche, Finanziarie e Assicurative¶Università di Roma “La Sapienza”¶Via del Castro Laurenziano 9, 00161 Roma, Italy, , , , , , IT

    Fausto Gozzi

  2. Space & Naval Warfare Systems Center, Code D73H¶San Diego, CA 92152-5001, USA, , , , , , US

    S. S. Sritharan

  3. School of Mathematics¶Georgia Institute of Technology¶Atlanta, GA 30332, USA, , , , , , US

    Andrzej Święch

Authors
  1. Fausto Gozzi
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  2. S. S. Sritharan
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  3. Andrzej Święch
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Accepted June 4, 2002¶Published online June 4, 2002

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Gozzi, F., Sritharan, S. & Święch, A. Viscosity Solutions of Dynamic-Programming Equations for the Optimal Control of the Two-Dimensional Navier-Stokes Equations. Arch. Rational Mech. Anal. 163, 295–327 (2002). https://doi.org/10.1007/s002050200203

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  • DOI: https://doi.org/10.1007/s002050200203

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