Abd-Allah Hyder1, 2, *, M. El-Badawy3
CMC-Computers, Materials & Continua, Vol.64, No.2, pp. 859-870, 2020, DOI:10.32604/cmc.2020.09897
Abstract In this paper, the non-stationary incompressible fluid flows governed by the
Navier-Stokes equations are studied in a bounded domain. This study focuses on the timefractional Navier-Stokes equations in the optimal control subject, where the control is
distributed within the domain and the time-fractional derivative is proposed as RiemannLiouville sort. In addition, the control object is to minimize the quadratic cost functional.
By using the Lax-Milgram lemma with the assistance of the fixed-point theorem, we
demonstrate the existence and uniqueness of the weak solution to this system. Moreover,
for a quadratic cost functional subject to the time-fractional Navier-Stokes equations, we
prove… More >
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