Cauchy problem for the non-newtonian viscous incompressible fluid

Pokorný, Milan. "Cauchy problem for the non-newtonian viscous incompressible fluid." Applications of Mathematics 41.3 (1996): 169-201. <http://eudml.org/doc/32944>.

@article{Pokorný1996,
abstract = {We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor $\tau ^V(\mathbb \{e\}) = \tau (\mathbb \{e\}) - 2\mu _1 \Delta \mathbb \{e\}$, where the nonlinear function $\tau (\mathbb \{e\})$ satisfies $\tau _\{ij\}(\mathbb \{e\})e_\{ij\} \ge c|\mathbb \{e\}|^p$ or $\tau _\{ij\}(\mathbb \{e\})e_\{ij\} \ge c(|\mathbb \{e\}|^2+|\mathbb \{e\}|^p)$. First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for $p > 1$ for both models. Then, under vanishing higher viscosity $\mu _1$, the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for $p > \frac\{3n\}\{n+2\}$, its uniqueness and regularity for $p \ge 1 + \frac\{2n\}\{n+2\}$. In the case of the second model the existence of the weak solution is proved for $p>1$.},
author = {Pokorný, Milan},
journal = {Applications of Mathematics},
keywords = {non-Newtonian incompressible fluids; Navier-Stokes equations; Cauchy problem; non-Newtonian fluids; bipolar fluids; existence, uniqueness, regularity of weak solution},
language = {eng},
number = {3},
pages = {169-201},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Cauchy problem for the non-newtonian viscous incompressible fluid},
url = {http://eudml.org/doc/32944},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Pokorný, Milan
TI - Cauchy problem for the non-newtonian viscous incompressible fluid
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 3
SP - 169
EP - 201
AB - We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor $\tau ^V(\mathbb {e}) = \tau (\mathbb {e}) - 2\mu _1 \Delta \mathbb {e}$, where the nonlinear function $\tau (\mathbb {e})$ satisfies $\tau _{ij}(\mathbb {e})e_{ij} \ge c|\mathbb {e}|^p$ or $\tau _{ij}(\mathbb {e})e_{ij} \ge c(|\mathbb {e}|^2+|\mathbb {e}|^p)$. First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for $p > 1$ for both models. Then, under vanishing higher viscosity $\mu _1$, the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for $p > \frac{3n}{n+2}$, its uniqueness and regularity for $p \ge 1 + \frac{2n}{n+2}$. In the case of the second model the existence of the weak solution is proved for $p>1$.
LA - eng
KW - non-Newtonian incompressible fluids; Navier-Stokes equations; Cauchy problem; non-Newtonian fluids; bipolar fluids; existence, uniqueness, regularity of weak solution
UR - http://eudml.org/doc/32944
ER -