Мішана задача для інтегро-диференціальних систем  Бусінеска-Стокса

Мар'яна Хома

Анотація


Розглянуто нелінійні параболічні системи зі змінними показниками нелінійності. Доведено теорему єдиності узагальненого розв'язку мішаної задачі для цієї системи.

Повний текст:

PDF

Посилання


R. Temam, Navier-Stokes equations: theory and numerical analysis, North-Holland Publ., Amsterdam, New York, Oxford, 1979.

J. Simon, Nonhomogeneous viscous incompressible fluids: existence of velocity, density and preassure, SIAM J. Math. Anal. 21 (1990), no. 5, 1093-1117. DOI: 10.1137/0521061

J. A. Langa, J. Real, and J. Simon, Existence and regularity of the pressure for the stochastic Navier-Stokes equations, Appl. Math. Optimization 48 (2003), no. 3, 195-210. DOI: 10.1007/s00245-003-0773-7

O. M. Buhrii, Visco-plastic, newtonian, and dilatant fluids: Stokes equations with variable exponent of nonlinearity, Mat. Studii 49 (2018), no. 2, 165-180.

O. Buhrii and N. Buhrii, Nonlocal in time problem for anisotropic parabolic equations with variable exponents of nonlinearities, J. Math. Anal. Appl. 473 (2019), no. 2, 695-711. DOI: 10.1016/j.jmaa.2018.12.058

M. Bokalo, O. Buhrii, and N. Hryadil, Initial-boundary value problems for nonlinear elliptic-parabolic equations with variable exponents of nonlinearity in unbounded domains without conditions at infinity, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 192 (2020), Article ID 111700, 17 p. DOI: 10.1016/j.na.2019.111700

J. R. Cannon and E. DiBenedetto, The initial value problem for the Boussinesq equations with data in Lp, Approximation methods for Navier-Stokes problems, Proc. Symp. IUTAM, Paderborn 1979, Lect. Notes Math. 771 (1980), 129-144.

C. Conca and M. A. Rojas-Medar, The initial value problem for the Boussinesq equations in a time-dependent domain, Technical report, Universidad de Chile. 1993. P. 1-16.

O. Buhrii and M. Khoma, On initial-boundary value problem for nonlinear integro-differential Stokes system, Visnyk Lviv Univ. Series Mech.-Math. 85 (2018), 107-119.

M. V. Khoma and O. M. Buhrii, Stokes system with variable exponents of nonlinearity, Буковин. мат ж. 10 (2022), no. 2, 28-42. DOI: 10.31861/bmj2022.02.03

O. Kovacik and I. Rakosnic, On spaces Lp(x),Wk,p(x), Czechosl. Math. J. 41 (1991), no. 4, 592-618.

W. Orlicz, Uber Konjugierte Exponentenfolgen, Stud. Math. 3 (1931), 200-211. DOI: 10.4064/sm-3-1-200-211

S. Antontsev and S. Shmarev, Evolution PDEs with nonstandard growth conditions. Existence, uniqueness, localization, blow-up, Atlantis Studies in Diff. Eq., Vol. 4, Paris: Atlantis Press, 2015.

L. Diening, P. Harjulehto, P. Hästö, and M. Růžička, Lebesgue and Sobolev spaces with variable exponents, Springer, Heidelberg, 2011.

X.-L. Fan and D. Zhao, On the spaces Lp(x)(Ω) and Wm,p(x)(Ω), J. Math. Anal. Appl. 263 (2001), no. 2, 424-446. DOI: 10.1006/jmaa.2000.7617

А. В. Гетлинг, Формирование пространственных структур конвекции Рэлея–Бенара, УФН, 161 (1991), no. 9, 1-80; English version: A. V. Getling, Formation of spatial structures in Rayleigh–Bénard convection, Sov. Phys. Usp. 34 (1991), no. 9, 737-776. DOI: 10.1070/PU1991v034n09ABEH002470

H. Sohr, The Navier-Stokes equations: an elementary functional analytic approach, Birkhauser, Boston, Basel, Berlin, 2001.




DOI: http://dx.doi.org/10.30970/vmm.2022.94.146-155

Посилання

  • Поки немає зовнішніх посилань.