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Asymptotic behavior of linearized viscoelastic flow problem
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The stochastic primitive equations in two space dimensions with multiplicative noise
Iterative method for mass diffusion model with density dependent viscosity
| 1. | Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain |
| 2. | Laboratoire d'Analyse Numérique et d'Informatique (LANI), Université Gaston Berger, BP 234, Saint-Louis, Senegal |
We use an iterative method to approach regular solutions. Moreover, some convergence rates are obtained, depending on weak, strong and more regular norms. This work extend to [1], where this technique has been used for the model with constant viscosity.
The model has a diffusive operator $-\lambda$div$(\rho (\nabla v +\nabla v^t))$ with $v$ the velocity field, which not allows us to use direct Stokes regularity (as has been done in [1]. Thus, it becomes more difficult to obtain the $H^2\times H^1$ and $H^3\times H^2$ regularity for the velocity-pressure pair $(v,p)$. The key is to use a new regularity result for a Stokes type problem with $\rho\Delta v$ as diffusion term.
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