Carleman estimate for the Navier–Stokes equations and an application to a lateral Cauchy problem

DOI10.1088/0266-5611/32/2/025001zbMath1339.35209arXiv1506.02534OpenAlexW624007727MaRDI QIDQ2794607

Mourad Bellassoued, Oleg Yurievich Imanuvilov, Masahiro Yamamoto

Publication date: 10 March 2016

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.02534

zbMATH Keywords

Navier-Stokes equationsCauchy problemCarleman estimate

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) Navier-Stokes equations (35Q30) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30)

Related Items (10)

Carleman estimate for the Navier–Stokes equations and applications ⋮ Stability estimate for scalar image velocimetry ⋮ Carleman estimates for a magnetohydrodynamics system and application to inverse source problems ⋮ Global Lipschitz stability for an inverse source problem for the Navier–Stokes equations ⋮ Quantification of the unique continuation property for the nonstationary Stokes problem ⋮ Data assimilation finite element method for the linearized Navier–Stokes equations in the low Reynolds regime ⋮ Inverse Problems for a Compressible Fluid System ⋮ Local solvability of an inverse problem to the Navier–Stokes equation with memory term ⋮ Inverse coefficient problem for a magnetohydrodynamics system by Carleman estimates ⋮ Identification of deformable droplets from boundary measurements: the case of non-stationary Stokes problem

Cites Work

• Unnamed Item
• Unnamed Item
• Weak and strong solutions of the Navier-Stokes initial value problem
• Quantification of the unique continuation property for the nonstationary Stokes problem
• A unique continuation theorem for second order parabolic differential operators
• Carleman estimates for parabolic equations with nonhomogeneous boundary conditions
• Unique continuation for some evolution equations
• Local exact controllability of the Navier-Stokes system
• Carleman estimates for coefficient inverse problems and numerical applications.
• Inverse boundary value problem for the Stokes and the Navier-Stokes equations in the plane
• Inverse viscosity problem for the Navier-Stokes equation
• Inverse source problem for linearized Navier–Stokes equations with data in arbitrary sub-domain
• Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
• Remark on boundary data for inverse boundary value problems for the Navier–Stokes equations
• Some questions in the qualitative theory of elliptic and parabolic equations

This page was built for publication: Carleman estimate for the Navier–Stokes equations and an application to a lateral Cauchy problem