Skip to main content
SpringerLink
Log in

Estimate from Below for the Growth of Solution to the Navier-Stokes Equation When the Solution Blows Up

  • Chapter
  • First Online:
Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 228))

  • 1444 Accesses

Abstract

Estimates for the growth of solution from below to the Navier- Stokes equation are provided.

Mathematics Subject Classification (2010). 35Q30.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.A. Adams, SobolevSp aces. Academic Press, New York 1973.

    Google Scholar 

  2. C. Fefferman, Navier-Stokes Equation. Clay Mathematical Institute, Official Problem Description, http://www.claymath.org/millennium/Navier-Stokes Equations, 2011.

  3. E. Gagliardo, Ulteriori proprietá di alcune classi di funzioni in piu variablili. Ricerche Mat. 8 (1959), 24–52.

    MathSciNet  MATH  Google Scholar 

  4. E. Hopf, Über die Anfangswertaufgaben der Hydrodynamik zäher Flüssigkeiten. Math. Nachrichten 4 (1950–1951), 213–231.

    Google Scholar 

  5. O.A. Ladizhenskaya, The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach Science Publishers, New York, London, Paris, 1969.

    Google Scholar 

  6. O.A. Ladizhenskaya, V.A. Solonnikov, and N.N. Ural’ceva, Linear and Quasi-linear Equations of Parabolic Type. American Mathematical Society, Providence, RI, 1968.

    Google Scholar 

  7. J.L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications. Dunod ⋅ Paris, 1968.

    Google Scholar 

  8. A.J. Majda and A.L. Bertozzi, Vorticity and Incompressible Flow. Cambridge University Press, 2002.

    Google Scholar 

  9. L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa 3 (13) (1959), 115–162.

    MathSciNet  Google Scholar 

  10. V.A. Solonnikov,On general boundary-value problem for elliptic systems in the sense of Douglis-Nirenberg, I. Izv. Akad. Nauk SSSR, ser. mat. 28 (1964), 665–706.

    Google Scholar 

  11. V.A. Solonnikov, On general boundary-value problem for elliptic systems in the sense of Douglis-Nirenberg, II. Trudy Mat. Inst. Steklov 92 (1966), 233–297.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto Politecnico Nacional – ESFM, Av. IPN S/N, U.P.A.L.M Edif. 9, C.P. 07738, Mexico, D.F., Mexico

    Valeri V. Kucherenko

Authors
  1. Valeri V. Kucherenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valeri V. Kucherenko .

Editor information

Editors and Affiliations

  1. de Morelos, Facultad de Ciencias, Universidad Autónoma del Estado, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, 62209, Morelos, Mexico

    Yuri I. Karlovich

  2. , Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino, 10123, Italy

    Luigi Rodino

  3. , Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Straße 39, Chemnitz, 09126, Germany

    Bernd Silbermann

  4. , Department of Mathematics, College of William and Mary, Jones Hall 114, Williamsburg, 23187-8795, Virginia, USA

    Ilya M. Spitkovsky

Additional information

Dedicated to the 70th birthday of the excellent scientist and great friend Vladimir Rabinovich

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Basel

About this chapter

Cite this chapter

Kucherenko, V.V. (2013). Estimate from Below for the Growth of Solution to the Navier-Stokes Equation When the Solution Blows Up. In: Karlovich, Y., Rodino, L., Silbermann, B., Spitkovsky, I. (eds) Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. Operator Theory: Advances and Applications, vol 228. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0537-7_12

Download citation

Publish with us

Policies and ethics

Search

Navigation