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  1. Journal of Mathematical Fluid Mechanics
  2. Journal of Mathematical Fluid Mechanics : Volume 8
  3. Journal of Mathematical Fluid Mechanics : Volume 8, Issue 1, February 2006
  4. Scherk-Type Capillary Graphs
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Journal of Mathematical Fluid Mechanics : Volume 19
Journal of Mathematical Fluid Mechanics : Volume 18
Journal of Mathematical Fluid Mechanics : Volume 17
Journal of Mathematical Fluid Mechanics : Volume 16
Journal of Mathematical Fluid Mechanics : Volume 15
Journal of Mathematical Fluid Mechanics : Volume 14
Journal of Mathematical Fluid Mechanics : Volume 13
Journal of Mathematical Fluid Mechanics : Volume 12
Journal of Mathematical Fluid Mechanics : Volume 11
Journal of Mathematical Fluid Mechanics : Volume 10
Journal of Mathematical Fluid Mechanics : Volume 9
Journal of Mathematical Fluid Mechanics : Volume 8
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 4, December 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 3, August 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 2, April 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 1, February 2006
Analyticity of Solutions to Nonlinear Parabolic Equations on Manifolds and an Application to Stokes Flow
About the Linear Stability of the Spherically Symmetric Solution for the Equations of a Barotropic Viscous Fluid under the Influence of Self-Gravitation
A Note on the Existence of Solutions to the Oseen System in Lipschitz Domains
The Fundamental Solution of the Linearized Navier–Stokes Equations for Spinning Bodies in Three Spatial Dimensions – Time Dependent Case
Scherk-Type Capillary Graphs
On the Structure of MHD Shock Waves in Diffusive-Dispersive Media
Journal of Mathematical Fluid Mechanics : Volume 7
Journal of Mathematical Fluid Mechanics : Volume 6
Journal of Mathematical Fluid Mechanics : Volume 5
Journal of Mathematical Fluid Mechanics : Volume 4
Journal of Mathematical Fluid Mechanics : Volume 3
Journal of Mathematical Fluid Mechanics : Volume 2
Journal of Mathematical Fluid Mechanics : Volume 1

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Scherk-Type Capillary Graphs

Content Provider SpringerLink
Author Huff, Robert McCuan, John
Copyright Year 2006
Abstract This paper concerns the regularity of a capillary graph (the meniscus profile of liquid in a cylindrical tube) over a corner domain of angle α. By giving an explicit construction of minimal surface solutions previously shown to exist (Indiana Univ. Math. J. 50 (2001), no. 1, 411–441) we clarify two outstanding questions.Solutions are constructed in the case α = π/2 for contact angle data (γ1, γ2) = (γ, π − γ) with 0 < γ < π. The solutions given with |γ − π/2| < π/4 are the first known solutions that are not C2 up to the corner. This shows that the best known regularity (C1, ∈) is the best possible in some cases. Specific dependence of the Hölder exponent on the contact angle for our examples is given.Solutions with γ = π/4 have continuous, but horizontal, normal vector at the corners in accordance with results of Tam (Pacific J. Math. 124 (1986), 469–482). It is shown that our examples are C0, β up to and including the corner for any β < 1.Solutions with |γ − π/2| > π/4 have a jump discontinuity at the corner. This kind of behavior was suggested by numerical work of Concus and Finn (Microgravity sci. technol. VII/2 (1994), 152–155) and Mittelmann and Zhu (Microgravity sci. technol. IX/1 (1996), 22–27). Our explicit construction, however, allows us to investigate the solutions quantitatively. For example, the trace of these solutions, excluding the jump discontinuity, is C2/3.
Ending Page 119
Page Count 21
Starting Page 99
File Format PDF
ISSN 14226928
e-ISSN 14226952
Journal Journal of Mathematical Fluid Mechanics
Issue Number 1
Volume Number 8
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2005-10-07
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword free surface minimal surface Mechanics, Fluids, Thermodynamics Mathematical Methods in Physics Fluids Capillarity Weierstrass representation mean curvature Capillarity (surface tension) wedge domain contact angle Minimal surfaces, surfaces with prescribed mean curvature
Content Type Text
Resource Type Article
Subject Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics
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