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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 8
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Research Article

Global Lipschitz stability for an inverse source problem for the Navier–Stokes equations

Oleg Y. Imanuvilova Department of Mathematics, Colorado State University, Fort Collins, CO, USAView further author information
&
M. Yamamotob Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Meguro, Japan;c Academy of Romanian Scientists, Ilfov, nr.3, Bucuresti, Romania;d Accademia Peloritana dei Pericolanti, Palazzo Università, Messina, Italy;e Peoples' Friendship University of Russia (RUDN University), Moscow, Russian FederationCorrespondence[email protected]
[email protected]
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Pages 2200-2210 | Received 19 Aug 2021, Accepted 10 Dec 2021, Published online: 30 Dec 2021

References

  • Imanuvilov OY, Yamamoto M. Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Probl. 1998;14:1229–1245.
  • Choulli M, Imanuvilov OY, Puel J-P, et al. Inverse source problem for linearized Navier-Stokes equations with data in arbitrary sub-domain. Appl Anal. 2013;92:2127–2143.
  • Bukhgeim AL, Klibanov MV. Global uniqueness of a class of multidimensional inverse problems. Soviet Math Dokl. 1981;24:244–247.
  • Beilina L, Klibanov MV. Approximate global convergence and adaptivity for coefficient inverse problems. Berlin: Springer-Verlag; 2012.
  • Bellassoued M, Yamamoto M. Carleman estimates and applications to inverse problems for hyperbolic systems. Tokyo: Springer-Japan; 2017.
  • Huang X, Imanuvilov OY, Yamamoto M. Stability for inverse source problems by Carleman estimates. Inverse Probl. 2020;36:125006.
  • Imanuvilov OY, Yamamoto M. Global Lipschitz stability in an inverse hyperbolic problem by interior observations. Inverse Probl. 2001;17:717–728.
  • Isakov V. Inverse source problems. Providence (RI): American Mathematical Society; 1990.
  • Klibanov MV. Inverse problems and Carleman estimates. Inverse Probl. 1992;8:575–596.
  • Klibanov MV, Timonov AA. Carleman estimates for coefficient inverse problems and numerical applications. Utrecht: VSP; 2004.
  • Yamamoto M. Carleman estimates for parabolic equations and applications. Inverse Probl. 2009;25:123013 (75pp).
  • Bellassoued M, Imanuvilov OY, Yamamoto M. Carleman estimate for the Navier-Stokes equations and an application to a lateral Cauchy problem. Inverse Probl. 2016;32:025001.
  • Fan J, Cristo MD, Jiang Y, et al. Inverse viscosity problem for the Navier-Stokes equation. J Math Anal Appl. 2010;365:750–757.
  • Fan J, Jiang Y, Nakamura G. Inverse problems for the Boussinesq system. Inverse Probl. 2009;25:085007. (10pp).
  • Imanuvilov OY, Lorenzi L, Yamamoto M. Carleman estimate for the Navier-Stokes equations and applications. Preprint. Available from: arXiv:2107.04495.
  • Imanuvilov OY, Yamamoto M. Inverse source problem for the Stokes system. In: Direct and inverse problems of mathematical physics (Newark, DE, 1997). Dordrecht: Kluwer Acad. Publ.; 2000. p. 441–451. (Int. Soc. Anal. Appl. Comput.; 5).
  • Imanuvilov OY, Yamamoto M. Inverse problems for a compressible fluid system. In: Inverse problems and related topics. Berlin: Springer-Verlag; 2020. p. 101–148. (Springer Proceedings in Mathematics & Statistics; 310).
  • Fernández-Cara E, Guerrero S, Imanuvilov OY, et al. Local exact controllability of the Navier-Stokes system.J Math Pures Appl. 2004;83:1501–1542.
  • Imanuvilov OY. Controllability of parabolic equations. Sbor Math. 1995;186:879–900.
  • Vogelsang V. On the strong unique continuation principle for inequalities of Maxwell type. Math Ann. 1991;289:285–295.
  • Imanuvilov OY, Puel J-P. Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems. Int Math Res Not. 2003;16:883–913.

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