Capillary surfaces and floating bodies

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• 作者：Josef Bemelmans (1)
  Giovanni P. Galdi (2)
  Mads Kyed (3)
  
• 关键词：Capillarity ; Variational problem for Caccioppoli sets ; 76B45
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：193
• 期：4
• 页码：1185-1200
• 全文大小：211 KB
• 参考文献：1. Bemelmans, J., Galdi, G.P., Kyed, M.: Fluid flows around floating bodies, I: the hydrostatic case. J. Math. Fluid Mech. 14, 751鈥?70 (2012)
  2. Emmer, M.: Esistenza, unicit脿 e regolarit脿 nelle superfici de equilibrio nei capillar. Ann. Univ. Ferrara Sez. VII (N.S.) 18, 79鈥?4 (1973)
  3. Massari, U., Miranda, M.: Minimal Surfaces of Codimension One. North-Holland, Amsterdam (1984)
  4. McCuan, J.: A variational formula for floating bodies. Pac. J. Math. 231(1), 167鈥?91 (2007) CrossRef
  5. Taylor, J.: Boundary regularity for solutions to various capillarity and free boundary problems. Commun. Partial Differ. Equ. 2, 323鈥?57 (1977) CrossRef
  
• 作者单位：Josef Bemelmans (1)
  Giovanni P. Galdi (2)
  Mads Kyed (3)
  
  1. Institut f眉r Mathematik, RWTH Aachen University, 52056 Aachen, Germany
  2. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 15261 Pittsburgh, PA, USA
  3. Department Mathematik, Friedrich-Alexander-Universit盲t Erlangen-N眉rnberg, 91058 Erlangen, Germany
  
• ISSN：1618-1891

文摘

We investigate capillary surfaces with boundary components on a floating body. The unknowns of this problem, the free surface and the position and orientation of the floating body are determined by minimizing the corresponding energy; besides gravitation and cohesion forces, we consider also adhesion between the fluid and both the wall of the container and the floating body. Existence of a solution is shown in the class of Caccioppoli sets under suitable restrictions on the data, as well as for surfaces that are graphs of real functions.