The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation
Year: 2002
Journal of Partial Differential Equations, Vol. 15 (2002), Iss. 2 : pp. 57–71
Abstract
The Boussinesq approximation, where the viscosity depends polynomially on the shear rate,finds more and more frequent use in geological practice. In this paper, we consider the periodic initial value problem and initial value problem for this modified Boussinesq approximation with the viscous part of the stress tensor τ^v = τ(e)- 2μΔe, where the nonlinear function τ(e) satisfies τ _{ij}(e)e_{ij} ≥ C|e|^p or τ_{ij}(e)e_{ij} ≥ C(|e|²+|e|^p). The existence, uniqueness and regularity of the weak solution is proved for p > \frac{2n}{n + 2}.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2002-JPDE-5448
Journal of Partial Differential Equations, Vol. 15 (2002), Iss. 2 : pp. 57–71
Published online: 2002-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: non-Newtonian incompressible fluids