scholarly journals A Priori Estimates for the Compressible Euler Equations for a Liquid with Free Surface Boundary and the Incompressible Limit

2017 ◽  
Vol 71 (7) ◽  
pp. 1273-1333 ◽  
Author(s):  
Hans Lindblad ◽  
Chenyun Luo
Keyword(s):  
Free Surface ◽  
Euler Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Compressible Euler Equations ◽  
Surface Boundary ◽  
Incompressible Limit ◽  
Priori Estimates ◽  
Compressible Euler

scholarly journals A priori estimates for a relativistic liquid with free surface boundary

2019 ◽  
Vol 16 (03) ◽  
pp. 401-442
Author(s):  
Daniel Ginsberg
Keyword(s):  
Free Surface ◽  
Fundamental Form ◽  
A Priori Estimates ◽  
Fluid Velocity ◽  
A Priori ◽  
Second Fundamental Form ◽  
Energy Estimates ◽  
Surface Boundary ◽  
The Second Fundamental Form ◽  
Sobolev Norms

We prove energy estimates for a relativistic free liquid body with sufficiently small fluid velocity in a general Lorentz spacetime. These estimates control Sobolev norms of the fluid velocity and enthalpy in the interior as well as Sobolev norms of the second fundamental form on the boundary. These estimates are generalizations of the energy estimates of Christodoulou and Lindblad [D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Commun. Pure Appl. Math. 53(12) (2000) 1536–1602] and rely on elliptic estimates which only require bounds for the second fundamental form of the time slices of the free boundary.

scholarly journals A PRIORI ESTIMATES FOR THE MOTION OF A SELF-GRAVITATING INCOMPRESSIBLE LIQUID WITH FREE SURFACE BOUNDARY

2009 ◽  
Vol 06 (02) ◽  
pp. 407-432 ◽  
Author(s):  
HANS LINDBLAD ◽  
KARL HÅKAN NORDGREN
Keyword(s):  
A Priori Estimates ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
A Priori ◽  
Time Interval ◽  
Surface Boundary ◽  
Priori Estimates ◽  
Moving Domain ◽  
Half Derivatives ◽  
Derivatives Of

In this paper, we prove a priori estimates in Lagrangian coordinates for the equations of motion of an incompressible, inviscid, self-gravitating fluid with free-boundary. The estimates show that on a finite time interval we control five derivatives of the fluid-velocity and five and a half derivatives of the coordinates of the moving domain.

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