A modification of the method of fictitious domains for stationary model of non-Newtonian liquids
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Keywords:
Fictitious domains, hydrodynamics, generalized solution, existence theorem.Abstract
The substantiation of one modification method of fictitious domains with continuation on junior coefficient for the stationary equations of non-Newtonian liquids is given in this work. The domain is three-dimensional and bounded. A theorem of an existence and convergence of the generalized solution of an auxiliary problem is proved. The theorem is proved by the method of a priori estimates. Inequality of imbedding theorems, Holder inequality and Young's inequality are used. The sequence of approximate solutions is constructed using the Galerkin method. The limit in the integral identity through the selected sequence. For solutions obtained uniform evaluation standards of functional spaces. An estimation of convergence of the strong solution of the approximating problem is deduced.References
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2. Turganbaev M.E. A filtration of a viscoelastic liquid of type Оldroyd’s // Dynamics of the continuous environment. – 1994 – Vol.108. – P.80-97. (in Russian)
3. Krykpaeva A.A. A method of fictitious domains for the non-Newtonian liquids equations. The Bulletin of KazSU, ser. math., mech., inf. – 2000. – №5(19). – P.92-97. (in Russian)
4. Antonsev C.N., Kazhihov A.V., Monahov V.N. Boundary problems of mechanics of non-uniform liquids // Novosibirsk: Nauka. – 1983. –318 p. (in Russian)
2. Turganbaev M.E. A filtration of a viscoelastic liquid of type Оldroyd’s // Dynamics of the continuous environment. – 1994 – Vol.108. – P.80-97. (in Russian)
3. Krykpaeva A.A. A method of fictitious domains for the non-Newtonian liquids equations. The Bulletin of KazSU, ser. math., mech., inf. – 2000. – №5(19). – P.92-97. (in Russian)
4. Antonsev C.N., Kazhihov A.V., Monahov V.N. Boundary problems of mechanics of non-uniform liquids // Novosibirsk: Nauka. – 1983. –318 p. (in Russian)
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Baytulenov, Z. B. (2015). A modification of the method of fictitious domains for stationary model of non-Newtonian liquids. International Journal of Mathematics and Physics, 6(2), 16–22. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/143
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Informatics and Mathematical Modeling
