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\begin{document}

\title{INVERSE PROBLEMS FOR NONLINEAR NAVIER-STOKES-VOIGT SYSTEM WITH MEMORY}



\author[1]{Khonatbek Khompysh}%
\author[1]{A.G. Shakir}%
\author[1]{A.A. Kabidoldanova}%
\affil[1]{Al-Farabi Kazakh National University}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\begin{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.%
\end{abstract}%



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