Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Existence and analyticity of Lei-Lin solution to the Navier-Stokes equations


Author: Hantaek Bae
Journal: Proc. Amer. Math. Soc. 143 (2015), 2887-2892
MSC (2000): Primary 35Q30, 76D03
DOI: https://doi.org/10.1090/S0002-9939-2015-12266-6
Published electronically: March 4, 2015
MathSciNet review: 3336613
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove the recent work of Lei-Lin in a slightly different setting, which enables us to prove analyticity of the solution.


References [Enhancements On Off] (What's this?)

  • [1] Hantaek Bae, Animikh Biswas, and Eitan Tadmor, Analyticity and decay estimates of the Navier-Stokes equations in critical Besov spaces, Arch. Ration. Mech. Anal. 205 (2012), no. 3, 963-991. MR 2960037, https://doi.org/10.1007/s00205-012-0532-5
  • [2] Animikh Biswas and David Swanson, Gevrey regularity of solutions to the 3-D Navier-Stokes equations with weighted $ l_p$ initial data, Indiana Univ. Math. J. 56 (2007), no. 3, 1157-1188. MR 2333469 (2008m:35261), https://doi.org/10.1512/iumj.2007.56.2891
  • [3] Marco Cannone, Ondelettes, paraproduits et Navier-Stokes, Diderot Editeur, Paris, 1995 (French). With a preface by Yves Meyer. MR 1688096 (2000e:35173)
  • [4] M. Cannone and F. Planchon, Self-similar solutions for Navier-Stokes equations in $ {\bf R}^3$, Comm. Partial Differential Equations 21 (1996), no. 1-2, 179-193. MR 1373769 (97a:35172), https://doi.org/10.1080/03605309608821179
  • [5] Jean-Yves Chemin, Théorèmes d'unicité pour le système de Navier-Stokes tridimensionnel, J. Anal. Math. 77 (1999), 27-50 (French). MR 1753481 (2001c:35185), https://doi.org/10.1007/BF02791256
  • [6]
    L. Escauriaza, G. Serigin, V. Sverak,
    $ L_{3,\infty }$ solutions of Navier-Stokes equations and backward uniquness,
    Uspekhi Mat. Nauk, 58 (2003), 3-44.
  • [7] C. Foias and R. Temam, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal. 87 (1989), no. 2, 359-369. MR 1026858 (91a:35135), https://doi.org/10.1016/0022-1236(89)90015-3
  • [8] Hiroshi Fujita and Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16 (1964), 269-315. MR 0166499 (29 #3774)
  • [9] Giulia Furioli, Pierre G. Lemarié-Rieusset, and Elide Terraneo, Unicité dans $ L^3(\mathbb{R}^3)$ et d'autres espaces fonctionnels limites pour Navier-Stokes, Rev. Mat. Iberoamericana 16 (2000), no. 3, 605-667 (French, with English and French summaries). MR 1813331 (2002j:76036), https://doi.org/10.4171/RMI/286
  • [10] Pierre Germain, Nataša Pavlović, and Gigliola Staffilani, Regularity of solutions to the Navier-Stokes equations evolving from small data in $ {\rm BMO}^{-1}$, Int. Math. Res. Not. IMRN 21 (2007), Art. ID rnm087, 35. MR 2352218 (2009d:76034), https://doi.org/10.1093/imrn/rnm087
  • [11] Zoran Grujić and Igor Kukavica, Space analyticity for the Navier-Stokes and related equations with initial data in $ L^p$, J. Funct. Anal. 152 (1998), no. 2, 447-466. MR 1607936 (99b:35168), https://doi.org/10.1006/jfan.1997.3167
  • [12] Rafaela Guberović, Smoothness of Koch-Tataru solutions to the Navier-Stokes equations revisited, Discrete Contin. Dyn. Syst. 27 (2010), no. 1, 231-236. MR 2600769 (2011d:35371), https://doi.org/10.3934/dcds.2010.27.231
  • [13] Tosio Kato, Strong $ L^{p}$-solutions of the Navier-Stokes equation in $ {\bf R}^{m}$, with applications to weak solutions, Math. Z. 187 (1984), no. 4, 471-480. MR 760047 (86b:35171), https://doi.org/10.1007/BF01174182
  • [14] Herbert Koch and Daniel Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math. 157 (2001), no. 1, 22-35. MR 1808843 (2001m:35257), https://doi.org/10.1006/aima.2000.1937
  • [15] Zhen Lei and Fanghua Lin, Global mild solutions of Navier-Stokes equations, Comm. Pure Appl. Math. 64 (2011), no. 9, 1297-1304. MR 2839302 (2012k:35391), https://doi.org/10.1002/cpa.20361
  • [16] P. G. Lemarié-Rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall/CRC Research Notes in Mathematics, vol. 431, Chapman & Hall/CRC, Boca Raton, FL, 2002. MR 1938147 (2004e:35178)
  • [17] Yves Le Jan and Alain Sol Sznitman, Cascades aléatoires et équations de Navier-Stokes, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 7, 823-826 (French, with English and French summaries). MR 1446587 (97m:60123), https://doi.org/10.1016/S0764-4442(97)86952-2
  • [18] Hideyuki Miura and Okihiro Sawada, On the regularizing rate estimates of Koch-Tataru's solution to the Navier-Stokes equations, Asymptot. Anal. 49 (2006), no. 1-2, 1-15. MR 2260554 (2007j:35160)
  • [19] Marcel Oliver and Edriss S. Titi, Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in $ {\bf R}^n$, J. Funct. Anal. 172 (2000), no. 1, 1-18. MR 1749867 (2000m:35147), https://doi.org/10.1006/jfan.1999.3550
  • [20] Fabrice Planchon, Asymptotic behavior of global solutions to the Navier-Stokes equations in $ {\bf R}^3$, Rev. Mat. Iberoamericana 14 (1998), no. 1, 71-93. MR 1639283 (99k:35144), https://doi.org/10.4171/RMI/235

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35Q30, 76D03

Retrieve articles in all journals with MSC (2000): 35Q30, 76D03


Additional Information

Hantaek Bae
Affiliation: Department of Mathematics, University of California Davis, Davis, California 95616
Email: hantaek@math.ucdavis.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12266-6
Keywords: Navier-Stokes equations, analyticity of mild solutions
Received by editor(s): May 5, 2013
Published electronically: March 4, 2015
Communicated by: Walter Craig
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society