Skip to main content
SpringerLink
Log in

Kato's perturbation theory and well-posedness for the Euler equations in bounded domains

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

References

  1. Beirão da Veiga, H., “On the solutions in the large of the two-dimensional flow of a nonviscous incompressible fluid”, J. Diff. Eq. 54 (1984) 373–389.

    Google Scholar 

  2. H. Beirão da Veiga, “Existence results in Sobolev spaces for a stationary transport equation”, U.T.M. 203—June 1986, Univ. of Trento. To appear in Ricerche di Matematica in the volume dedicated to the memory of Professor C. Miranda.

  3. H. Beirão da Veiga, “Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow”, Rend. Sem. Mat. Univ. Padova 79 (1988).

  4. H. Beirão da Veiga, “A well-posedness theorem for nonhomogeneous inviscid fluids via a perturbation theorem”, to appear in J. Diff. Eq.

  5. D. G. Ebin, “A concise presentation of the Euler equations of hydrodynamics”, Comm. Partial Diff. Eq. 9 (1984), 539–559.

    Google Scholar 

  6. D. G. Ebin, “The equations of motion of a perfect fluid with free boundary are not well posed”, Comm. Partial Diff. Eq. 12 (1987), 1175–1201.

    Google Scholar 

  7. D. G. Ebin & E. Marsden, “Groups of diffeomorphisms and the motion of an incompressible fluid”, Ann. of Math. 92 (1970), 102–163.

    Google Scholar 

  8. T. Kato, “Linear evolution equations of ‘hyperbolic’ type”, J. Fac. Sci. Univ. Tokyo 17 (1970), 241–258.

    Google Scholar 

  9. T. Kato, “Linear evolution equations of ‘hyperbolic’ type, II”, J. Math. Soc. Japan 25 (1973), 648–666.

    Google Scholar 

  10. T. Kato, “Quasi-linear equations of evolution, with applications to partial differential equations”, Lecture Notes in Mathematics, No. 448, pp. 25–70. Springer, New York, 1975.

    Google Scholar 

  11. T. Kato & C. Y. Lai, “Nonlinear evolution equations and the Euler flow”, J. Funct. Analysis 56 (1984), 15–28.

    Google Scholar 

  12. T. Kato & G. Ponce, “Commutator estimates and the Euler and Navier-Stokes equations”, (to appear).

  13. R. Temam, “On the Euler equations of incompressible perfect fluids”, J. Funct. Analysis 20 (1975), 32–43.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Matematiche Applicate “U. Dini”, Università di Pisa, Italy

    H. Beirão da Veiga

Authors
  1. H. Beirão da Veiga
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by H. Brezis

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beirão da Veiga, H. Kato's perturbation theory and well-posedness for the Euler equations in bounded domains. Arch. Rational Mech. Anal. 104, 367–382 (1988). https://doi.org/10.1007/BF00276432

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00276432

Keywords

Search

Navigation