Skip to main content
SpringerLink
Log in

On Backward Uniqueness for Parabolic Equations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We prove a backward uniqueness result for the heat operator with variable lower order terms, which implies the full regularity of L 3,∞-solutions of the three-dimensional Navier–Stokes equations. Bibliography: 12 titles.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. S. Alinhac and M. S. Baouendi, “Uniqueness for the characteristic Cauchy problem and strong unique continuation for higher order partial differential inequalities,” Amer. J. Math., 102, 179-217 (1980).

    Google Scholar 

  2. L. Escauriaza, “Carleman inequalities and the heat operator,” Duke Math. J., 104, 113-126 (2000).

    Google Scholar 

  3. L. Escauriaza and F. J. Fernández, “Unique continuation for parabolic operators” (to appear).

  4. L. Escauriaza and L. Vega, “Carleman inequalities and the heat operator. II,” Indiana Univ. Math. J., 50, 1149-1169 (2001).

    Google Scholar 

  5. F. J. Fernández, “Unique continuation for parabolic operators. II” (to appear).

  6. L. Hörmander, Linear Partial Differential Operators, Springer-Verlag (1963).

  7. L. Hörmander, “Uniqueness theorems for second order elliptic differential equations,” Comm. PDE, 8, 21-64 (1983).

    Google Scholar 

  8. T. Kato, “Strong L p-solutions of the Navier–Stokes equations in R m with applications to weak solutions,” Math. Zeit. 187, 471-480 (1984).

    Google Scholar 

  9. O. A. Ladyzhenskaya, Mathematical Problems of the Dynamics of Viscous Incompressible Fluids, Gorden and Breach (1969).

  10. S. Micu and E. Zuazua, “On the lack of null-controllability of the heat equation on the half-space,” Portugaliae Mathematica, 58, 1-24 (2001).

    Google Scholar 

  11. G. Seregin and V. Šverák, “Navier–Stokes and backward uniqueness for the heat equation,” IMA preprint No. 1852 (April 2002), downloadable from http://www.ima.umn.edu.

  12. F. Trèves, Linear Partial Differential Equations, Gordon and Breach (1970).

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del País, Vasco, Spain

    L. Escauriaza

  2. St.Petersburg Department of the Steklov Mathematical Institute, U.S.A

    G. Seregin

  3. School of Mathematics, University of Minnesota, USA

    V. Šverák

Authors
  1. L. Escauriaza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Seregin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Šverák
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Escauriaza, L., Seregin, G. & Šverák, V. On Backward Uniqueness for Parabolic Equations. Journal of Mathematical Sciences 123, 4577–4579 (2004). https://doi.org/10.1023/B:JOTH.0000041475.11233.d8

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOTH.0000041475.11233.d8

Keywords

Search

Navigation