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On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem

Author

Listed:
  • Francesca Crispo

    (Università degli Studi della Campania “L. Vanvitelli”)

  • Paolo Maremonti

    (Università degli Studi della Campania “L. Vanvitelli”)

Abstract

The paper is concerned with the Navier–Stokes Cauchy problem. We investigate on some results of regularity and uniqueness related to suitable weak solutions corresponding to a special set of initial data. The suitable weak solution notion is meant in the sense introduced by Caffarelli–Kohn–Nirenberg. As further result we discuss the uniqueness of a set of suitable weak solutions (wider than the previous one) enjoying a “Prodi–Serrin” condition which is “relaxed” in space.

Suggested Citation

  • Francesca Crispo & Paolo Maremonti, 2021. "On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem," Partial Differential Equations and Applications, Springer, vol. 2(3), pages 1-36, June.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:3:d:10.1007_s42985-021-00073-z
    DOI: 10.1007/s42985-021-00073-z
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    Cited by:

    1. Yasushi Taniuchi, 2021. "A remark on the uniqueness of Kozono–Nakao’s mild $$L^3$$ L 3 -solutions on the whole time axis to the Navier–Stokes equations in unbounded domains," Partial Differential Equations and Applications, Springer, vol. 2(5), pages 1-16, October.

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