AIMS Mathematics, 2019, 4(3): 516-526. doi: 10.3934/math.2019.3.516

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Identification of the source term in Navier-Stokes system with incomplete data

1 Department of Mathematics, University of 08 May 1945, Guelma, Algeria
2 Department of Mathematics, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria

The aim of this work is to get instantaneous information at fixed instant T on pollution term in Navier-Stokes system in which the initial condition is incomplete. The best method which can solve this problem is the sentinel method; It allows estimating the pollution term at which we look for information independently of the missing term that we do not want to identify. So, we prove the existence of such instantaneous sentinel by solving a problem of controllability with constraint on the control.
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