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

Berhail Amel; Rezzoug Imad; Berhail Amel; Rezzoug Imad

doi:10.3934/math.2019.3.516

AIMS Mathematics

2019, Volume 4, Issue 3: 516-526. doi: 10.3934/math.2019.3.516

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Research article

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

Berhail Amel ¹,
Rezzoug Imad ^{2
,
,}

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

Received: 19 February 2019 Accepted: 12 May 2019 Published: 27 May 2019
MSC : 93B05, 49J20, 76D05

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.
- controllability,
- control optimal,
- Navier-Stokes system,
- instantaneous sentinel,
- pollution term
Citation: Berhail Amel, Rezzoug Imad. Identification of the source term in Navier-Stokes system with incomplete data[J]. AIMS Mathematics, 2019, 4(3): 516-526. doi: 10.3934/math.2019.3.516

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Abstract

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.

References

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