Open AccessSolvability of initial boundary value problems for equations describing motions of linear viscoelastic fluids
Author(s) -
N. A. Karazeeva
Publication year - 2005
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/jam.2005.59
Subject(s) - mathematics , viscoelasticity , boundary value problem , mathematical analysis , nonlinear system , compressibility , cauchy stress tensor , operator (biology) , non newtonian fluid , generalized newtonian fluid , newtonian fluid , tensor (intrinsic definition) , boundary (topology) , initial value problem , viscosity , classical mechanics , physics , mechanics , geometry , shear rate , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor , thermodynamics
The nonlinear parabolic equations describing motion of incompressible media are investigated. The rheological equations of most general type are considered. The deviator of the stress tensor is expressed as a nonlinear continuous positive definite operator applied to the rate of strain tensor. The global-in-time estimate of solution of initial boundary value problem is obtained. This estimate is valid for systems of equations of any non-Newtonian fluid. Solvability of initial boundary value problems for such equations is proved under some additional hypothesis. The application of this theory makes it possible to prove the existence of global-in-time solutions of two-dimensional initial boundary value problems for generalized linear viscoelastic liquids, that is, for liquids with linear integral rheological equation, and for third-grade liquids
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