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The Initialization Problem for the Equations of Incompressible Asymmetric Fluids

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Abstract

We investigate the initialization problem for the incompressible asymmetric fluids equations in two space dimensions. The problem is formulated as an optimal control problem. We prove that this problem has at least one and at most finite many solutions. Finally, we determine sufficient conditions to assure uniqueness of the solution.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Brazil

    P. Braz e Silva & C. Cunha

  2. Universidade Federal do Piauí, Parnaíba, Brazil

    C. Cunha

  3. Departamento de Matemática, Universidade de Tarapacá, Arica, Chile

    M. A. Rojas-Medar

Authors
  1. P. Braz e Silva
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  2. C. Cunha
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  3. M. A. Rojas-Medar
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Correspondence to P. Braz e Silva.

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P. Braz e Silva: Partially supported by CAPES-PRINT, Brazil, #8881.311964/2018-01 and CNPq, Brazil, #308758/2018-8 and #432387/2018-8. C. Cunha: Partially supported by CAPES-PRINT, Brazil, #8881.311964/2018-01. M. A. Rojas-Medar: Partially supported by CAPES-PRINT, Brazil, #8881.311964/2018-01.

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Braz e Silva, P., Cunha, C. & Rojas-Medar, M.A. The Initialization Problem for the Equations of Incompressible Asymmetric Fluids. Appl Math Optim 84, 1317–1340 (2021). https://doi.org/10.1007/s00245-020-09678-z

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