On the Euler equations for nonhomogeneous fluids (I)

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1. [1] S.N. Antoncev - A.V. Kazhikhov, Mathematical study of flows of non homogeneous fluids, Novosibirsk, Lectures at the University, 1973 (russian). MR421289
2. [2] H. Beirão Da Veiga - A. Valli, On the motion of a non-homogeneous ideal incompressible fluid in an external force field, Rend. Sem. Mat. Padova, 59 (1978), pp. 117-145. Zbl0433.76001MR547082
3. [3] H. Beirão Da Veiga - A. Valli, On the Euler equations for non-homogeneous fluids (II), to appear in J. Math. Anal. Appl. Zbl0503.76008MR563987
4. [4] H. Beirão Da Veiga - A. Valli, Existence of C∞ solutions of the Euler equations for non-homogeneous fluids, to appear in Comm. Partial Diff. E q. Zbl0437.35059
5. [5] D. Gilbarg - N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin- Heidelberg, 1977. Zbl0361.35003MR473443
6. [6] D. Graffi, Il teorema di unicità per i fluidi incompressibili, perfetti, eterogenei, Rev. Un. Mat. Argentina, 17 (1955), pp. 73-77. Zbl0074.20206MR82829
7. [7] P. Hartman, Ordinary differential equations, J. Wiley and Sons, Inc., Baltimore, 1973. Zbl0125.32102MR344555
8. [8] E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 4 (1950-51), pp. 213-231. Zbl0042.10604MR50423
9. [9] T. Kato, On classical solutions of the two-dimensional non-stationary Euler equation, Arch. Rat. Mech. Anal., 25 (1967), pp. 188-200. Zbl0166.45302MR211057
10. [10] A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Physics Dokl., 19 (1974), pp. 331-332 (previously in Dokl. Akad. Nauk. SSSR, 216 (1974), pp. 1008-1010 (russian)). Zbl0307.76011MR430562
11. [11] O.A. Lady - V.A. Solonnikov, The unique solvability of an initial-boundary value problem for viscous, incompressible, inhomogeneous fluids, Zap. Naučn. Sem. Leningrad, 52 (1975), pp. 52-109, pp. 218-219 (russian) (translated in Journal of Soviet Mathematics, 9 (1978)). Zbl0376.76021MR425391
12. [12] O.A. Lady - N.N. Ural'ceva, Equations aux derivées partielles de type elliptique, Dunod, Paris, 1968 (translated from russian). MR239273
13. [13] P.H. Le Blond - L.A. Mysak, Waves in the ocean, Elsevier, Amsterdam, 1977. 
14. [14] J.L. Lions, On some questions in boundary value problems of Mathematical Physics, Rio de Janeiro, Lectures at the Univ. Federal, Instituto de Mat., 1977. Zbl0404.35002MR519648
15. [15] 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
16. [16] C. Miranda, Sul problema misto per le equazioni lineari ellittiche, Ann. Mat. Pura Appl., 39 (1955), pp. 279-303. Zbl0066.34301MR78561
17. [17] C. Miranda, Partial Differential Equations of Elliptic Type, Second revised edition, Springer-Verlag, Berlin-Heidelberg, 1970. Zbl0198.14101MR284700
18. [18] L. Sédov, Mécanique des milieux continus, vol. I, Editions MIR, Moscow (1975) (translated from russian). 
19. [19] R. Temam, On the Euler equations of incompressible perfect fluids, J. Funct. Anal., 20 (1975), pp. 32-43. Zbl0309.35061
20. [20] K.-O. Widman, Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand., 21 (1967), pp. 17-37. Zbl0164.13101MR239264
21. [21] W. Wolibner, Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long, Math. Z., 37 (1933), pp. 698-726. Zbl0008.06901MR1545430
22. [22] C.-S. Yih, Dynacmics of nonhomogeneous fluids, The Macmillan Co., New York, 1965. Zbl0193.55205MR183194
23. [23] R.K. Zeytounian, Notes sur les Ecoulements Rotationnels de Fluids Parfaits, Lecture Notes in Physics n. 27, Springer-Verlag, Berlin-Heidelberg, 1974. Zbl0292.76021
24. [24] J. Simon, Écoulement d'un fluide non homogène avec une densité initiale s'annullant, C. R. Acad. Sc. Paris, 287 (1978), pp. 1009-1012. Zbl0395.76038MR519229

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