Volume 15, Issue 2
The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation

Boling Guo & Yadong Shang

J. Part. Diff. Eq., 15 (2002), pp. 57-71.

Published online: 2002-05

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  • 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}.
  • Keywords

non-Newtonian incompressible fluids Boussinesq approximation periodic initial value problem initial value problem weak solution

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@Article{JPDE-15-57, author = {}, title = {The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {2}, pages = {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}.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5448.html} }
TY - JOUR T1 - The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation JO - Journal of Partial Differential Equations VL - 2 SP - 57 EP - 71 PY - 2002 DA - 2002/05 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5448.html KW - non-Newtonian incompressible fluids KW - Boussinesq approximation KW - periodic initial value problem KW - initial value problem KW - weak solution AB - 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}.
Boling Guo & Yadong Shang . (2019). The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation. Journal of Partial Differential Equations. 15 (2). 57-71. doi:
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