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Recovering a Constant in the Two-Dimensional Navier–Stokes System with No Initial Condition

Recovering a Constant in the Two-Dimensional Navier–Stokes System with No Initial Condition We deal with the $$2D$$ 2 D -Navier–Stokes system endowed with Cauchy boundary conditions, but with no initial condition. We assume that the right-hand side is of the form $$\beta f_0+f_1$$ β f 0 + f 1 , where $$\beta \in \mathbb {R}$$ β ∈ R is an unknown constant. To determine $$\beta $$ β we are given a functional involving the velocity field $$y$$ y . First we prove uniqueness for the pair $$(y,\beta )$$ ( y , β ) , via suitable weak Carleman estimates, and then we show the locally Lipschitz-continuous dependence of $$(y,\beta )$$ ( y , β ) on the data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Recovering a Constant in the Two-Dimensional Navier–Stokes System with No Initial Condition

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-014-9261-5
Publisher site
See Article on Publisher Site

Abstract

We deal with the $$2D$$ 2 D -Navier–Stokes system endowed with Cauchy boundary conditions, but with no initial condition. We assume that the right-hand side is of the form $$\beta f_0+f_1$$ β f 0 + f 1 , where $$\beta \in \mathbb {R}$$ β ∈ R is an unknown constant. To determine $$\beta $$ β we are given a functional involving the velocity field $$y$$ y . First we prove uniqueness for the pair $$(y,\beta )$$ ( y , β ) , via suitable weak Carleman estimates, and then we show the locally Lipschitz-continuous dependence of $$(y,\beta )$$ ( y , β ) on the data.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Oct 1, 2014

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