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Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces

  • Jamel Benameur EMAIL logo and Lotfi Jlali
Published/Copyright: July 24, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 4

Abstract

In this paper, we prove a global well-posedness of the three-dimensional incompressible Navier-Stokes equation under initial data, which belongs to the Lei-Lin-Gevrey space Za,σ−1(ℝ3) and if the norm of the initial data in the Lei-Lin space 𝓧−1 is controlled by the viscosity. Moreover, we will show that the norm of this global solution in the Lei-Lin-Gevrey space decays to zero as time approaches to infinity.

Keywords: Navier-Stokes equations; critical spaces; long time decay
MSC 2010: 35-xx; 35Bxx; 35Lxx

  1. (Communicated by Andras Ronto)

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Received: 2019-02-05
Accepted: 2020-01-15
Published Online: 2020-07-24
Published in Print: 2020-08-26

© 2020 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. Some relative normality properties in locales
  3. Upper bounds of some special zeros for the Rankin-Selberg L-function
  4. Factorization of polynomials over valued fields based on graded polynomials
  5. Varieties of ∗-regular rings
  6. On reverse Hölder and Minkowski inequalities
  7. Coefficient inequalities related with typically real functions
  8. Existence of wandering and periodic domain in given angular region
  9. The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
  10. Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
  11. Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
  12. Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
  13. 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
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  15. The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
  16. Multi-opponent James functions
  17. An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
  18. A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
  19. On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
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https://doi.org/10.1515/ms-2017-0400
Keywords for this article
Navier-Stokes equations; critical spaces; long time decay

Articles in the same Issue

  1. Regular papers
  2. Some relative normality properties in locales
  3. Upper bounds of some special zeros for the Rankin-Selberg L-function
  4. Factorization of polynomials over valued fields based on graded polynomials
  5. Varieties of ∗-regular rings
  6. On reverse Hölder and Minkowski inequalities
  7. Coefficient inequalities related with typically real functions
  8. Existence of wandering and periodic domain in given angular region
  9. The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
  10. Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
  11. Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
  12. Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
  13. 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
  14. More on closed non-vanishing ideals in CB(X)
  15. The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
  16. Multi-opponent James functions
  17. An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
  18. A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
  19. On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
  20. Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
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