An Existence Theorem for Weak Solutions of the Initial–Boundary Value Problem for the Inhomogeneous Incompressible Kelvin–Voigt Model in Which the Initial Value of Density is Not Bounded from Below
Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 628-632 Cet article a éte moissonné depuis la source Math-Net.Ru

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Keywords: hydrodynamics, Kelvin–Voigt model, inhomogeneous fluid, weak solution, existence theorem.
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V. G. Zvyagin; M. V. Turbin. An Existence Theorem for Weak Solutions of the Initial–Boundary Value Problem for the Inhomogeneous Incompressible Kelvin–Voigt Model in Which the Initial Value of Density is Not Bounded from Below. Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 628-632. http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a11/

[1] A. V. Kazhikhov, Dokl. AN SSSR, 216:5 (1974), 1008–1010 | MR | Zbl

[2] J. Simon, SIAM J. Math. Anal., 21:5 (1990), 1093–1117 | DOI | MR

[3] R. J. DiPerna, P.-L. Lions, Invent. Math., 98:3 (1989), 511–547 | DOI | MR

[4] P.-L. Lions, Mathematical Topics in Fluid Mechanics, v. 1, Oxford Lecture Ser. Math. Appl., 3, Incompressible Models, Clarendon Press, Oxford, 1996 | MR

[5] V. G. Zvyagin, M. V. Turbin, Gidrodinamika, SMFN, 31, RUDN, M., 2009, 3–144 | MR

[6] A. P. Oskolkov, Kraevye zadachi matematicheskoi fiziki. 13, Tr. MIAN SSSR, 179, 1988, 126–164 | MR | Zbl

[7] C. Amrouche, L. C. Berselli, R. Lewandowski, D. D. Nguyen, Nonlinear, 196 (2020), Article 111790 | DOI | MR

[8] A. V. Zvyagin, Matem. zametki, 105:6 (2019), 839–856 | DOI | MR

[9] A. V. Zvyagin, V. P. Orlov, Matem. zametki, 97:5 (2015), 681–698 | DOI | MR

[10] A. Ustiuzhaninova, M. Turbin, J. Dyn. Control Syst., 28:3 (2022), 465–480 | DOI | MR

[11] M. Turbin, A. Ustiuzhaninova, Evol. Equ. Control Theory, 11:6 (2022), 2055–2072 | DOI | MR

[12] S. N. Antontsev, H. B. de Oliveira, Kh. Khompysh, Nonlinearity, 34:5 (2021), 3083–3111 | DOI | MR

[13] V. G. Zvyagin, M. V. Turbin, Dokl. RAN. Matem., inform., prots. upr., 509 (2023), 13–16 | DOI

[14] V. Zvyagin, M. Turbin, J. Fixed Point Theory Appl., 23:1 (2021), Article 4 | MR

[15] V. G. Zvyagin, M. V. Turbin, Izv. vuzov. Matem., 2020, no. 4, 93–98 | DOI

[16] V. G. Zvyagin, Trudy Shestoi Mezhdunarodnoi konferentsii po differentsialnym i funktsionalno-differentsialnym uravneniyam (Moskva, 2011), SMFN, 46, RUDN, M., 2012, 92–119

[17] R. Temam, Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR

[18] J. Simon, Ann. Mat. Pura Appl. (4), 146 (1987), 65–96 | DOI | MR