Existence theorems for compressible viscous fluids having zero shear viscosity
Rendiconti del Seminario Matematico della Università di Padova, Tome 71 (1984), pp. 73-102. 
@article{RSMUP_1984__71__73_0,
     author = {Secchi, Paolo},
     title = {Existence theorems for compressible viscous fluids having zero shear viscosity},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {73--102},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {71},
     year = {1984},
     mrnumber = {769429},
     zbl = {0563.76067},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_1984__71__73_0/}
}
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Secchi, Paolo. Existence theorems for compressible viscous fluids having zero shear viscosity. Rendiconti del Seminario Matematico della Università di Padova, Tome 71 (1984), pp. 73-102. http://archive.numdam.org/item/RSMUP_1984__71__73_0/

[1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions Il, Comm. Pure Appl. Math., 17 (1964), pp. 35-92. | MR | Zbl

[2] H. Beirão Da Veiga, On the barotropic motion of compressible perfect fluids, Ann. Sc. Norm. Sup. Pisa, 8 (1981), pp. 317-351. | EuDML | Numdam | MR | Zbl

[3] H. Beirão Da Veiga - A. Valli, On the Euler equations for nonhomogeneous fluids (I), preprint Univ. Trento.

[4] J.P. Bourguignon - H. Brezis, Remarks on the Euler equations, J. Funct. Anal., 15 (1974), pp. 341-363. | MR | Zbl

[5] S. Chapman - T.G. Cowling, The mathematical theory of non-uniform gases, third ed., Cambridge, 1970. | Zbl

[6] C. Foias - R. Temam, Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation, Ann. Sc. Norm. Sup. Pisa, 5 (1978), pp. 29-63. | EuDML | Numdam | MR | Zbl

[7] N. Itaya, On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluids, Kodai Math. Sem. Rep., 23 (1971), 60-120. | MR | Zbl

[8] T. Kato, Linear and quasi-linear equations of evolution of hyperbolic type, Corso CIME on « Hyperbolicity » (1976), pp. 127-191. | Zbl

[9] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'Ceva, Linear and quasi-linear equations of parabolic type, Amer. Math. Soc., Transl. Math. Mono., 23 (1968) (translated from Russian). | MR | Zbl

[10] J.L. Lions - E. Magenes, Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968. | MR | Zbl

[11] J.L. Lions E. Magenes, Problèmes aux limites non homogènes et applications, vol. 2, Dunod, Paris, 1968. | MR | Zbl

[12] A. Matsumura - T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), pp. 67-104. | MR | Zbl

[13] J. Nash, Le problème de Cauchy pour les équations différentielles d'un fluide général, Boll. Soc. Math. France, 90 (1962), pp. 487-497. | Numdam | MR | Zbl

[14] L. Rosenhead (and others), A discussion on the first and the second viscosities of fluids, Proc. Roy. Soc. Lond., Ser. A, 226 (1954), pp. 1-69. | MR

[15] J. Serrin, Mathematical principles of classical fluid mechanics, Handbuch der Physik, vol. VIII/1, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959. | MR

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

[17] V.A. Solonnikov, Solvability of the initial-boundary value problem for the equations of motion of a viscous compressible fluid, J. Soviet Math., 14 (1980), pp. 1120-1133 (previously in Zap-Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 56 (1976), pp. 128-142 [Russian]). | MR | Zbl

[18] V.A. Solonnikov - A.V. Kazhikhov, Existence theorems for the equations of motion of a compressible viscous fluid, Ann. Rev. Fluid Mech., 13 (1981), pp. 79-95. | Zbl

[19] A. Tani, On the first initial-boundary value problem of compressible viscous fluid motion, Publ. RIMS, Kyoto Univ., 13 (1977), pp. 193-253. | Zbl

[20] A. Valli, An existence theorem for compressible viscous fluids, Ann. Mat. Pura App., 130 (1982), pp. 197-213. | MR | Zbl

[21] A. Valli, A correction to the paper «An existence theorem for compressible viscous fluids », Ann. Mat. Pura Appl., 132 (1982), pp. 399-400. | MR | Zbl

[22] A. Valli, Uniqueness theorems for compressible viscous fluids, especially when the Stokes relation holds, Boll. Un. Mat. It., Anal. Funz. Appl., 18-C (1981), pp. 317-325. | MR | Zbl

[23] A.I. Yol'Pert - S.I. Hudjaev, On the Cauchy problem for composite systems of nonlinear differential equations, Math. USSR Sbornik, 16 (1972), pp. 517-544 (previously in Mat. Sbornik, 87 (1972), pp. 504-528 [Russian]). | MR | Zbl