On the motion of a non-homogeneous ideal incompressible fluid in an external force field

Hugo Beirão da Veiga; Alberto Valli

Rendiconti del Seminario Matematico della Università di Padova (1978)

  • Volume: 59, page 117-145
  • ISSN: 0041-8994

How to cite

top

Beirão da Veiga, Hugo, and Valli, Alberto. "On the motion of a non-homogeneous ideal incompressible fluid in an external force field." Rendiconti del Seminario Matematico della Università di Padova 59 (1978): 117-145. <http://eudml.org/doc/107671>.

@article{BeirãodaVeiga1978,
author = {Beirão da Veiga, Hugo, Valli, Alberto},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {non-homogeneous ideal incompressible fluid; external force field; Euler equations; local solution; Riemannian geometry on infinite dimensional manifolds; existence; Schauder's fixed point theorem; methods of Kato and McGrath},
language = {eng},
pages = {117-145},
publisher = {Seminario Matematico of the University of Padua},
title = {On the motion of a non-homogeneous ideal incompressible fluid in an external force field},
url = {http://eudml.org/doc/107671},
volume = {59},
year = {1978},
}

TY - JOUR
AU - Beirão da Veiga, Hugo
AU - Valli, Alberto
TI - On the motion of a non-homogeneous ideal incompressible fluid in an external force field
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1978
PB - Seminario Matematico of the University of Padua
VL - 59
SP - 117
EP - 145
LA - eng
KW - non-homogeneous ideal incompressible fluid; external force field; Euler equations; local solution; Riemannian geometry on infinite dimensional manifolds; existence; Schauder's fixed point theorem; methods of Kato and McGrath
UR - http://eudml.org/doc/107671
ER -

References

top
  1. [1] C. Bardos, Existence et unicité de la solution de l'équation d'Euler en dimension deux, J. Math. Anal. Appl., 40 (1972), pp. 769-790. Zbl0249.35070MR333488
  2. [2] K.K. Golovkin, Vanishing viscosity in Cauchy's problem for hydro-mechanics equations, Proc. Steklov Inst. Math., 92 (1966), pp. 33-53 (previously in Trudy Mat. Inst. Steklov, 92 (1966), pp. 31-49 [russian]). Zbl0168.35504MR207281
  3. [3] E. Hölder, Über die unbeschränkte Fortsetzbarkeit einer stetigen ebenen Bewegung in einer unbegrenzten inkompressiblen Flüssigkeit, Math. Z., 37 (1933), pp. 727-738. Zbl0008.06902MR1545431
  4. [4] E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 4 (1950-51), pp. 213-231. Zbl0042.10604MR50423
  5. [5] T. Kato, On Classical Solutions of the Two-Dimensional Non-Stationary Euler Equation, Arch. Rat. Mech. Anal., 25 (1967), pp. 188-200. Zbl0166.45302MR211057
  6. [6] J. Leray, Sur les mouvements des liquides illimites, C.R.A.S. Paris, 194 (1932), 1892-1894. Zbl0004.31701JFM58.0884.04
  7. [7] L. Lichtenstein, Neuere entwicklung der Potentialtheorie. Konforme Abbildung, Encycl. Math. Wiss., IIC3 (1918), pp. 177-377. JFM47.0450.01
  8. [8] J.E. Marsden, Well-posedness of the equations of a non-homogeneous perfect fluid, Comm. Partial Diff. Eq., 1 (1976), pp. 215-230. Zbl0341.35019MR405493
  9. [9] F.J. M, Nonstationary Plane Flow of Viscous and Ideal Fluids, Arch. Rat. Mech. Anal., 27 (1967), pp. 329-348. Zbl0187.49508MR221818
  10. [10] A.C. Schaeffer, Existence theorem for the flow of an ideal incompressible fluid in two dimensions, Trans. Amer. Math. Soc., 42 (1937), pp. 497-513. Zbl0018.12902MR1501931JFM63.0766.05
  11. [11] J. Serrin, On the uniqueness of compressible fluid motions, Arch. Rat. Mech. Anal., 3 (1959), pp. 271-288. Zbl0089.19103MR106646
  12. [12] A. Valli, Soluzioni classiche dell'equazione di Eulero dei fluidi bidimensionali in domini con frontiera variabile, Ricerche di Mat., 26 (1977), pp. 301-333. Zbl0421.76010MR479010
  13. [13] W. Wolibner, Un theorème sur l'esistence du mouvement plan d'un fluide parfait, homogène. incompressible, pendant un temps infiniment long, Math. Z., 37 (1933), pp. 698-726. Zbl0008.06901MR1545430
  14. [14] V.I. Yudovich, Non-stationary flows of ideal incompressible fluids, Zhur. Vych. Mat. i Mat. Fiz., 3 (1963), pp. 1032-1066 [russian]. Zbl0129.19402MR158189
  15. [15] V.I. Yudovich, A two dimensional problem of unsteady flow of an ideal incompressible fluid across a given domain, Amer. Math. Soc. Translations, 57 (1966), pp. 277-304 (previously in Mat. Sb., 64 (1964), pp. 562-588 [russian]). Added in proof: the analytic case in compact manifolds without boundary was studied in MR177577
  16. [16] M.S. Baouendi - C. Goulaouic, Solutions analytiques de l'equation d'Euler d'un fluide incompressible, Seminaire Goulaouic-Schwartz, 1976-77 (Paris). Zbl0361.35019

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.