On the motion of a non-homogeneous ideal incompressible fluid in an external force field
Rendiconti del Seminario Matematico della Università di Padova, Volume 59  (1978), p. 117-145
@article{RSMUP_1978__59__117_0,
     author = {Beir\~ao Da Veiga, Hugo and Valli, Alberto},
     title = {On the motion of a non-homogeneous ideal incompressible fluid in an external force field},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {59},
     year = {1978},
     pages = {117-145},
     zbl = {0433.76001},
     mrnumber = {547082},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1978__59__117_0}
}
Beirão da Veiga, Hugo; 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, Volume 59 (1978) , pp. 117-145. http://www.numdam.org/item/RSMUP_1978__59__117_0/

[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. | MR 333488 | Zbl 0249.35070

[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]). | MR 207281 | Zbl 0168.35504

[3] E. Hölder, Über die unbeschränkte Fortsetzbarkeit einer stetigen ebenen Bewegung in einer unbegrenzten inkompressiblen Flüssigkeit, Math. Z., 37 (1933), pp. 727-738. | MR 1545431 | Zbl 0008.06902

[4] E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 4 (1950-51), pp. 213-231. | MR 50423 | Zbl 0042.10604

[5] T. Kato, On Classical Solutions of the Two-Dimensional Non-Stationary Euler Equation, Arch. Rat. Mech. Anal., 25 (1967), pp. 188-200. | MR 211057 | Zbl 0166.45302

[6] J. Leray, Sur les mouvements des liquides illimites, C.R.A.S. Paris, 194 (1932), 1892-1894. | JFM 58.0884.04

[7] L. Lichtenstein, Neuere entwicklung der Potentialtheorie. Konforme Abbildung, Encycl. Math. Wiss., IIC 3 (1918), pp. 177-377. | JFM 47.0450.01

[8] J.E. Marsden, Well-posedness of the equations of a non-homogeneous perfect fluid, Comm. Partial Diff. Eq., 1 (1976), pp. 215-230. | MR 405493 | Zbl 0341.35019

[9] F.J. M, Nonstationary Plane Flow of Viscous and Ideal Fluids, Arch. Rat. Mech. Anal., 27 (1967), pp. 329-348. | MR 221818 | Zbl 0187.49508

[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. | JFM 63.0766.05 | MR 1501931

[11] J. Serrin, On the uniqueness of compressible fluid motions, Arch. Rat. Mech. Anal., 3 (1959), pp. 271-288. | MR 106646 | Zbl 0089.19103

[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. | MR 479010 | Zbl 0421.76010

[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. | MR 1545430 | Zbl 0008.06901

[14] V.I. Yudovich, Non-stationary flows of ideal incompressible fluids, Zhur. Vych. Mat. i Mat. Fiz., 3 (1963), pp. 1032-1066 [russian]. | MR 158189 | Zbl 0129.19402

[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 | MR 177577

[16] M.S. Baouendi - C. Goulaouic, Solutions analytiques de l'equation d'Euler d'un fluide incompressible, Seminaire Goulaouic-Schwartz, 1976-77 (Paris). | Numdam | Zbl 0361.35019