Article
A decomposition result for the pressure of a fluid in a thin domain and extensions to elasticity problems
Author/s | Casado Díaz, Juan
Luna Laynez, Manuel Suárez Grau, Francisco Javier |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2020-01 |
Deposit Date | 2024-09-09 |
Abstract | In order to study the asymptotic behavior of a fluid in a domain of small thickness $\ep$, it is common to use that the norm of the pressure $p_\ep$ in $L^q$, $q>1$, is smaller than $C\|\nabla p_\ep\|_{W^{-1,q}}/\ep$. Our ... In order to study the asymptotic behavior of a fluid in a domain of small thickness $\ep$, it is common to use that the norm of the pressure $p_\ep$ in $L^q$, $q>1$, is smaller than $C\|\nabla p_\ep\|_{W^{-1,q}}/\ep$. Our purpose in the present paper is to improve this estimate by showing that in fact $p_\ep$ can be decomposed as the sum of two terms: the first one is of order $1/\ep$ with respect to $\nabla p_\ep$ but it belongs to the Sobolev space $W^{1,q}$ and not only to $L^q$; the second one only belongs to $L^q$ but it is of order one with respect to $\nabla p_\ep$. This result also allows us to improve the classical estimate for Korn's constant in an elastic thin domain providing a decomposition of the deformation which contains terms with a stronger regularity. The advantage of these expansions is that they simplify the study of the asymptotic behavior of continuum mechanics problems in thin domains since they give an additional compactness. As examples we provide two applications in fluid mechanics and linear elasticity. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España |
Project ID. | MTM2014-53309-P
MTM2017- 83583-P |
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Casado-Luna-Suarez-Revised.pdf | 494.9Kb | [PDF] | View/ | Versión aceptada |