Optimal three-ball inequalities and quantitative uniqueness for the Stokes system

Lin, Ching-Lung; Uhlmann, Günther; Wang, Jenn‐Nan

doi:10.3934/dcds.2010.28.1273

Cited by 25 publications

(43 citation statements)

References 16 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, there is not so much results available on quantitative uniqueness for systems. About Stokes system we shall mention the works of Boulakia et al in [9,10] for stability estimates and of Ballerini in [6] and Lin et al in [26] for some other connected results.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability estimates for Navier-Stokes equations and application to inverse problems

Badra¹,

Caubet²,

Dardé³

2016

DCDS-B

View full text Add to dashboard Cite

In this work, we present some new Carleman inequalities for Stokes and Oseen equations with non-homogeneous boundary conditions. These estimates lead to log type stability inequalities for the problem of recovering the solution of the Stokes and Navier-Stokes equations from both boundary and distributed observations. These inequalities fit the well-known unique continuation result of Fabre and Lebeau [18]: the distributed observation only depends on interior measurement of the velocity, and the boundary observation only depends on the trace of the velocity and of the Cauchy stress tensor measurements. Finally, we present two applications for such inequalities. First, we apply these estimates to obtain stability inequalities for the inverse problem of recovering Navier or Robin boundary coefficients from boundary measurements. Next, we use these estimates to deduce the rate of convergence of two reconstruction methods of the Stokes solution from the measurement of Cauchy data: a quasi-reversibility method and a penalized Kohn-Vogelius method.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability estimates for Navier-Stokes equations and application to inverse problems

Badra¹,

Caubet²,

Dardé³

2016

DCDS-B

View full text Add to dashboard Cite

show abstract

“…In the second case stability may be proven in the form of a three balls inequality and associated local stability estimates, see [19,5]. For completeness of the analysis we focus on the second case for the error estimates below.…”

Section: Stokes Equationsmentioning

confidence: 99%

Stabilized nonconforming finite element methods for data assimilation in incompressible flows

Burman

Hansbo

2017

Math. Comp.

View full text Add to dashboard Cite

show abstract

“…In a recent paper by Lin, Uhlmann and Wang ( [14]), the validity of the three spheres inequality has been extended to solutions u = (u 1 , . .…”

Section: )mentioning

confidence: 99%

Stable determination of a body immersed in a fluid: the nonlinear stationary case

Ballerini

2013

Applicable Analysis

View full text Add to dashboard Cite

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier-Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log-log type. (2010): Primary 35R30. Secondary 35Q35, 76D07, 74F10. H 1 2 (∂Ω) Mathematical Subject Classification

show abstract

Optimal three-ball inequalities and quantitative uniqueness for the Stokes system

Cited by 25 publications

References 16 publications

Stability estimates for Navier-Stokes equations and application to inverse problems

Stability estimates for Navier-Stokes equations and application to inverse problems

Stabilized nonconforming finite element methods for data assimilation in incompressible flows

Stable determination of a body immersed in a fluid: the nonlinear stationary case

Contact Info

Product

Resources

About