Carleman estimate for the NavierStokes equations and an application to a lateral Cauchy problem
Abstract
We consider the nonstationary linearized NavierStokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the NavierStokes equations and prove the Hölder stability in determining the velocity and pressure field in an interior domain. In the final section, we apply the results for the linearized NavierStokes equations to the fully nonlinear NavierStokes equations and establish a similar Hölder stability estimate within sufficiently smooth solutions, and prove the uniqueness of LerayHopf weak solutions by surface stresses on an arbitrarily chosen subboundary.
 Publication:

Inverse Problems
 Pub Date:
 February 2016
 DOI:
 10.1088/02665611/32/2/025001
 arXiv:
 arXiv:1506.02534
 Bibcode:
 2016InvPr..32b5001B
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 doi:10.1088/02665611/32/2/025001