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On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluid. (English) Zbl 0219.76080

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
45E05 Integral equations with kernels of Cauchy type
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[1] BERGMANN, S., Integral operators in the theory of linear partial differential equa-tions. Springer-Verlag, Berlne (1961). · Zbl 0093.28701
[2] BERS, L., Mathematical aspects of subsonic and transonic gas dynamics. Joh Wiley & Sons, Inc., New York (1958). · Zbl 0083.20501
[3] CATTABRIGA, L., Su un problema al contorno relativo al sistema di equazioni d Stokes. Rend. Sem. Mat. Univ. Padova 31 (1961), 1-33. · Zbl 0116.18002 · numdam:RSMUP_1961__31__308_0 · eudml:107065
[4] CODDINGTON, E. A., AND N. LEviNsoN, Theory of ordinary differential equations McGraw-Hill, New York (1955). · Zbl 0064.33002
[5] COURANT, R., AND D. HiLBERT, Methods of mathematical physics, II. Interscience, New York (1962)
[6] 3HeJibMa, C., apa6oJiHqece CHCTMbi. MocKea (1964)
[7] FINN, R., On steady-state solutions of the Navier-Stokes partial differential equa tions. Arch. Rat. Mech. Anal. 3 (1959), 381-396. · Zbl 0104.42305 · doi:10.1007/BF00284188
[8] FINN, R., Stationary solutions of the Navier-Stokes equations. Proc. Symposi Appl. Math. 17 (1965), 121-153. · Zbl 0148.21602
[9] FRIEDMAN, A., Partial differential equations of parabolic type. Prentice Hal (1964). · Zbl 0144.34903
[10] FRIEDMAN, A., Generalized functions and partial differential equations. Prentic Hall (1963). · Zbl 0116.07002
[11] FUJITA, H., On the existence and regularity of the steady-state solutions of th Navier-Stokes equation. J. Fac. Sci. Univ. Tokyo 9 (1961), 59-102. · Zbl 0111.38502
[12] FUJITA, H., AND T. KATO, On the Navier-Stokes initial value problem, I. Arch Rat. Mech. Anal. 16 (1964), 269-315. · Zbl 0126.42301 · doi:10.1007/BF00276188
[13] FUKUHARA, M., Ordinary differential equations. Iwanami, Tokyo (1950). (Japanese
[14] jiyuiKO, B. . H C . KpeflH, po6Hbie creneHH HepeHHHaJibHbix opepaxopO H xeopeMbi B*eHHH. AH. CCCP 122 (1958), 963-966.
[15] GOLDSTEIN, S., Lectures on fluid mechanics.(Lectures in applied mathematics), Interscience Publishers, London (1960) · Zbl 0098.16703
[16] HOPF, E., Uber die Anfangswertaufgabe fur die hydrodynamischen Grundglei chungen. Math. Nachr. 4 (1951), 213-231. · Zbl 0042.10604 · doi:10.1002/mana.3210040121
[17] Io, S., The existence and uniqueness of regular solution of non-stationar Navier-Stokes equation. J. Fac. Sci. Univ. Tokyo, Sec. I. 9 (1961), 103-140. · Zbl 0116.17905
[18] KATO, T., Fractional powers of dissipative operators.J. Math. Soc. Japan 1 (1961), 305-308. · Zbl 0113.10005 · doi:10.2969/jmsj/01330246
[19] KATO, T., A generalization of the Heintz inequality. Proc. Jap. Acad. 37 (1961), 305-308 · Zbl 0104.09304 · doi:10.3792/pja/1195523678
[20] KATO, T., AND H. FUJITA, On the non-stationary Navier-Stokes system. Rend Sem. Mat. Univ. Padova 32 (1962), 243-260. · Zbl 0114.05002 · numdam:RSMUP_1962__32__243_0 · eudml:107082
[21] KaHTpoBHH, JI. B., H. AKHJIOB, yHKUHOHaJibHb anajins E HOpMHpOBaHHbi pocTpacTBax. MocKBa (H3MarHs) (1958).
[22] KceeB, A. A., H O. A. JIaAbieHca5i, O cymecTBOBaHHH H eAHHCTBeHOCT peiiieiiHH HecaiHHapHfi sa^an H BHCKOH HeoKHMaeMofi KHKOCTH. H. A. H. CCCP 21 (1957), 655-680. · Zbl 0078.39801
[23] KpacHOcejibCKHH, M. A., H . E. Co6o;eBcHH, po6bie cxeeHH oepaop AeficTByiomHX B aaxoBbix pocpacBa. ibid. 129 (1958), 499-502.
[24] JIaAbi>eHca5i, O A., B. A. COJIOHHHKOB, H H. H. ypajibijesa, JlHHeftHbie ypaBHCHHH apa6oiHHecoro aMocKBa (1967).
[25] LADYZHENSKAYA, 0. A., The mathematical theory of viscous incompressible flow Gordon and Breach (1963). · Zbl 0121.42701
[26] LERAY, J., Etude de diverses equations integrates non-lineaires et quelques pro blemes que pose I’hydrodynarmque. J. Math. Pures Appl., (IX) 12 (1933), 1-82. Zentralblatt MATH: · Zbl 0006.16702 · eudml:235182
[27] LERAY, J., Sur le mouvement d’un liquide visqueux emplissant espace. Act Math. 63 (1934), 193-248. · JFM 60.0726.05
[28] LERAY, J., Essai sur les mouvements plans d’un liquide visqueux que limiten des parois. J. Math. Pures Appl. (IX) 13 (1934), 331-418. · JFM 60.0727.01
[29] LICHTENSTEIN, L., Grundlagen der Hydromechanik. Julius Springer, Berlin (1929) · Zbl 0157.56701
[30] LIONS, J. L., Sur existence de solution des equations de Navier-Stokes. C. R. Acad. Sci. Paris 248 (1959), 2478-2850 · Zbl 0090.08203
[31] LIONS, J. L., Quelques resultats d’existence dans des equations aux devee partielles non-lineaires. Bull. Soc. Math. France 87 (1957), 245-283. · Zbl 0147.07902 · numdam:BSMF_1959__87__245_0 · eudml:86957
[32] NAGUMO, M., Differential equations, I. Kyoritsu, Tokyo (1955). (Japanese
[33] epBCKHH, H. ., JIeuHH 06 ypasneHKHX c HacimiMH POHSBOAHBIMH. oc HS , MecKBa (1953).
[34] PRANDTL, L., Proc. 3rd Inter. Math. Congr. Heidelberg (1904), reprinted in ”Vie Abhandlungen zur Hydro- und Aerodynamik”. Gttmgen (1927).
[35] PRANDTL, L., The mechanics of viscous fluids. Part G of Vol. III of aerodynami theory (W. F. Durand Ed.), Julius Springer, Berlin (1935).
[36] Co6ojieBCKHH, E., O. HecxauHOHapHbix ypaBeHx HpoHHaMHKH BHSKO SCHKOC. ibid. 128 (1959), 45-48.
[37] Co6oji3BCKHH, E., O. rjaKc o6o6meHHbix peiueH HaBbe-Coa. ibid. 13 (1951), 758-760.
[38] TERASAWA, K. (compiled), An outline of mathematics for natural scientists, Vol of applications. Iwanami, Tokyo (1961).(Japanese)
[39] TIKHONOV, A., Ein Fixpunktsatz. Math. Ann. III (1935), 767-776 · Zbl 0012.30803 · doi:10.1007/BF01472256 · eudml:159810
[40] ZEMANSKY, M. W., Heat and thermodynamics. McGraw-Hill, New York (1957) · Zbl 0077.39901
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