TY  - JOUR
ID  - 2007-17
T1  - Mathematical analysis of unsteady flows of fluids with pressure, shear-rate, and temperature dependent material moduli that slip at solid boundaries
A1  - Bulíček, Miroslav
A1  - Málek, Josef
A1  - Rajagopal, K. R.
JA  - SIAM J. Math. Anal.
Y1  - 2009
VL  - 41
IS  - 2
SP  - 665
EP  - 707
SN  - 0036-1410
N1  - Preprint no. 2007-17
UR  - http://www.karlin.mff.cuni.cz/ncmm/preprints/07176085904BuMaRa300507SIAM.pdf
M2  - doi: 10.1137/07069540X
KW  - existence result for large data
KW  - Generalized Navier-Stokes-Fourier system
KW  - Incompressible fluids
KW  - Navier’s slip boundary condition
KW  - Pressure-dependent viscosity
KW  - shear-dependent viscosity
KW  - suitable weak solution
KW  - temperature-dependent viscosity
KW  - unsteady flows
KW  - weak solution
N2  - In Bridgman's treatise [The Physics of High Pressures, MacMillan, New York, 1931], he carefully documented that the viscosity and the thermal conductivity of most liquids depend on the pressure and the temperature. The relevant experimental studies show that even at high pressures the variations of the values in the density are insignificant in comparison to that of the viscosity, and it is thus reasonable to assume that the liquids in question are incompressible fluids with pressure dependent viscosities. We rigorously investigate the mathematical properties of unsteady three-dimensional internal flows of such incompressible fluids. The model is expressed through a system of partial differential equations representing the balance of mass, the balance of linear momentum, the balance of energy, and the equation for the entropy production. Assuming that we have Navier's slip at the impermeable boundary we establish the long-time existence of a (suitable) weak solution when the data are large.
M1  - fjournal={SIAM Journal on Mathematical Analysis}
M1  - 
mrclass={76D03 (35Q35 76A05)}
M1  - 
mrnumber={MR2515781}
ER  -