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Inverse problems for nonlinear Navier–Stokes–Voigt system with memory

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  • Khompysh, Kh.
  • Shakir, A.G.
  • Kabidoldanova, A.A.

Abstract

This paper deals with the unique solvability of some inverse problems for nonlinear Navier–Stokes–Voigt (Kelvin–Voigt) system with memory that governs the flow of incompressible viscoelastic non-Newtonian fluids. The inverse problems that study here, consist of determining a time dependent intensity of the density of external forces, along with a velocity and a pressure of fluids. As an additional information, two types of integral overdetermination conditions over space domain are considered. The system supplemented also with an initial and one of the boundary conditions: stick and slip boundary conditions. For all inverse problems, under suitable assumptions on the data, the global and local in time existence and uniqueness of weak and strong solutions were established.

Suggested Citation

  • Khompysh, Kh. & Shakir, A.G. & Kabidoldanova, A.A., 2023. "Inverse problems for nonlinear Navier–Stokes–Voigt system with memory," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923010846
    DOI: 10.1016/j.chaos.2023.114182
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    References listed on IDEAS

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    1. N. A. Karazeeva, 2005. "Solvability of initial boundary value problems for equations describing motions of linear viscoelastic fluids," Journal of Applied Mathematics, Hindawi, vol. 2005, pages 1-22, January.
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