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Let us consider a system 13.1 \(\displaystyle \begin{aligned} \begin{array}{rclll} \partial _{t}\mathbf{v}-\nu\varDelta \mathbf{v}+\left(\mathbf{v}\cdot\nabla \right)\mathbf{v}+\nabla q & = & \tilde{\mathbf{f}} & \mbox{in} & {\mathcal D}(t),\,t\in\left(0,\infty\right)\,\\ \mbox{div }\mathbf{v} & = & 0 & \mbox{in} & {\mathcal D}(t),\,t\in \left(0,\infty\right)\\ \mathbf{v}(\mathbf{y},t) & = & \mathbf{V}(\mathbf{y},t) & \mbox{on} & \partial {\mathcal D} (t),\,t\in\left(0,\infty\right)\,\\ \mathbf{v}(\mathbf{y},t) & \rightarrow & {\boldsymbol 0} & \mbox{as} & |\mathbf{y}|\rightarrow\infty\end{array} {}\end{aligned} \) in a time-dependent exterior domain \({\mathcal D}(t) \subset { \mathbb R}^3\) .

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Appendix

  • 章节

  • 发表日期：

    2025年

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  • Šárka Nečasová,
  • Stanislav Kračmar,
  • Jiří Neustupa,
  • Patrick Penel

摘要

Let us consider a system 13.1 \(\displaystyle \begin{aligned} \begin{array}{rclll} \partial _{t}\mathbf{v}-\nu\varDelta \mathbf{v}+\left(\mathbf{v}\cdot\nabla \right)\mathbf{v}+\nabla q & = & \tilde{\mathbf{f}} & \mbox{in} & {\mathcal D}(t),\,t\in\left(0,\infty\right)\,\\ \mbox{div }\mathbf{v} & = & 0 & \mbox{in} & {\mathcal D}(t),\,t\in \left(0,\infty\right)\\ \mathbf{v}(\mathbf{y},t) & = & \mathbf{V}(\mathbf{y},t) & \mbox{on} & \partial {\mathcal D} (t),\,t\in\left(0,\infty\right)\,\\ \mathbf{v}(\mathbf{y},t) & \rightarrow & {\boldsymbol 0} & \mbox{as} & |\mathbf{y}|\rightarrow\infty\end{array} {}\end{aligned} \) in a time-dependent exterior domain \({\mathcal D}(t) \subset { \mathbb R}^3\) .