On the Navier–Stokes system with the Coulomb friction law boundary condition

详细信息    查看全文

• 作者：Loredana Bălilescu ; Jorge San Martín…
• 关键词：Navier–Stokes system ; Cauchy theory ; Coulomb’s law
• 刊名：Zeitschrift für angewandte Mathematik und Physik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：68
• 期：1
• 全文大小：
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1420-9039
• 卷排序：68

文摘

We propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier–Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two-dimensional problem and the existence of at least one solution in the three-dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method, and we present numerical simulations in two physical examples.