scholarly journals Local existence for the free boundary problem for nonrelativistic and Relativistic compressible Euler equations with a vacuum boundary condition

2009 ◽  
Vol 62 (11) ◽  
pp. 1551-1594 ◽  
Author(s):  
Yuri Trakhinin
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Boundary Problem ◽  
Euler Equations ◽  
Free Boundary Problem ◽  
Local Existence ◽  
Compressible Euler Equations ◽  
Compressible Euler

Local existence with low regularity for the 2D compressible Euler equations

2021 ◽  
Vol 18 (03) ◽  
pp. 701-728
Author(s):  
Huali Zhang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Euler Equations ◽  
Local Existence ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Spatial Derivative ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Local Solutions

We prove the local existence, uniqueness and stability of local solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial data of velocity, density, specific vorticity [Formula: see text] and the spatial derivative of specific vorticity [Formula: see text].

A free boundary problem arising in the modelling of internal oxidation of binary alloys

1995 ◽  
Vol 6 (3) ◽  
pp. 225-245
Author(s):  
Bei Hu ◽  
Jianhua Zhang
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Internal Oxidation ◽  
Free Boundary Problem ◽  
Binary Alloys ◽  
Local Existence ◽  
Discontinuous Coefficients ◽  
Parabolic Partial Differential Equation ◽  
One Dimensional ◽  
A Free Boundary Problem

A one-dimensional free boundary problem arising in the modelling of internal oxidation of binary alloys is studied in this paper. The free boundary of this problem is determined by the equation u = 0, where u is the solution of a parabolic partial differential equation with discontinuous coefficients across the free boundary. Local existence, uniqueness and the regularity of the free boundary are established. Global existence is also studied.

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