Well-Posedness of Vortex Sheets with Surface Tension

2003 ◽  
Vol 35 (1) ◽  
pp. 211-244 ◽  
Author(s):  
David M. Ambrose
Keyword(s):  
Surface Tension ◽  
Well Posedness ◽  
Vortex Sheets

scholarly journals Well-posedness of 3D vortex sheets with surface tension

2007 ◽  
Vol 5 (2) ◽  
pp. 391-430 ◽  
Author(s):  
David M. Ambrose ◽  
Nader Masmoudi
Keyword(s):  
Surface Tension ◽  
Well Posedness ◽  
Vortex Sheets

scholarly journals The Muskat problem with surface tension and equal viscosities in subcritical $$L_p$$-Sobolev spaces

2021 ◽  
Author(s):  
Anca-Voichita Matioc ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Global Existence Of Solutions ◽  
Muskat Problem ◽  
The Mathematical Model ◽  
Quasilinear Parabolic

AbstractIn this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $$W^s_p(\mathbb {R})$$ W p s ( R ) , where $${p\in (1,2]}$$ p ∈ ( 1 , 2 ] and $${s\in (1+1/p,2)}$$ s ∈ ( 1 + 1 / p , 2 ) . This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $$W^{\overline{s}-2}_p(\mathbb {R})$$ W p s ¯ - 2 ( R ) , where $${\overline{s}\in (1+1/p,s)}$$ s ¯ ∈ ( 1 + 1 / p , s ) . Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.

scholarly journals Traveling waves from the arclength parameterization: Vortex sheets with surface tension

2013 ◽  
Vol 15 (3) ◽  
pp. 359-380 ◽  
Author(s):  
Benjamin Akers ◽  
David Ambrose ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Traveling Waves ◽  
Vortex Sheets

scholarly journals A moving boundary problem for the Stokes equations involving osmosis: Variational modelling and short-time well-posedness

2015 ◽  
Vol 27 (4) ◽  
pp. 647-666
Author(s):  
FRIEDRICH LIPPOTH ◽  
MARK A. PELETIER ◽  
GEORG PROKERT
Keyword(s):  
Surface Tension ◽  
Boundary Problem ◽  
Osmotic Pressure ◽  
Moving Boundary ◽  
Stokes Equations ◽  
Semipermeable Membrane ◽  
Moving Boundary Problem ◽  
Classical Solutions ◽  
Well Posedness ◽  
Short Time

Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For this problem we prove the existence of classical solutions for a short-time.

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