Interface evolution: water waves in 2-D (Q1043491)
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scientific article; zbMATH DE number 5840878
- The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
| Language | Label | Description | Also known as |
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| English | Interface evolution: water waves in 2-D |
scientific article; zbMATH DE number 5840878 |
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Interface evolution: water waves in 2-D (English)
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The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces (English)
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9 December 2009
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24 January 2011
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This paper deals with the initial value problem for water waves, which consists of describing the motion of the free boundary between two irrotational, incompressible, and inviscid fluids under the influence of gravity in two-dimensional case without surface tension. It is considered two types of geometries of free boundary: periodicity in horizontal space variable and the case of a closed contour. The unknown function is the free boundary curve \(z(\alpha,t)\) and the vorticity \(\omega\) supported on the free boundary. The authors formulate the problem under consideration as initial value problem for the system of nonlocal integro-differential equations and prove local existence of a weak solution.
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free boundary
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Euler equations
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Rayleigh-Taylor
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local existence
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Euler
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Hele-Shaw-muskat
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incompressible
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well-possedness
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0.88585263
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0.8848126
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0.8757928
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0.87258303
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0.87113875
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0.87073255
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0.87011874
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