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Strong Unique Continuation for the Navier–Stokes Equation with Non-Analytic Forcing

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Abstract

We establish the strong unique continuation property for differences of solutions to the Navier–Stokes system with Gevrey forcing. For this purpose, we provide Carleman-type inequalities with the same singular weight for the Laplacian and the heat operator.

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Acknowledgments

The authors thank referees for useful remarks and suggestions. MI was supported in part by the NSF Grant DMS-1009769 and the NSF FRG Grant DMS-11589, while IK was supported in part by the NSF Grant DMS-1009769.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Mihaela Ignatova

  2. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    Igor Kukavica

Authors
  1. Mihaela Ignatova
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  2. Igor Kukavica
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Correspondence to Mihaela Ignatova.

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Ignatova, M., Kukavica, I. Strong Unique Continuation for the Navier–Stokes Equation with Non-Analytic Forcing. J Dyn Diff Equat 25, 1–15 (2013). https://doi.org/10.1007/s10884-012-9282-1

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  • DOI: https://doi.org/10.1007/s10884-012-9282-1

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