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Abstract The equation for a traveling wave on the boundary of a two‐dimensional droplet of an ideal fluid is derived by using the conformal variables technique for free surface waves. The free surface is subject only to the force of surface tension and the fluid flow is assumed to be potential. We use the canonical Hamiltonian variables discovered and map the lower complex plane to the interior of a fluid droplet conformally. The equations in this form have been originally discovered for infinitely deep water and later adapted to a bounded fluid domain.The new class of solutions satisfies a pseudodifferential equation similar to the Babenko equation for the Stokes wave. We illustrate with numerical solutions of the time‐dependent equations and observe the linear limit of traveling waves in this geometry.
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Initial data for first-order causal viscous conformal fluids in general relativity
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of the equations, even for constant-mean curvature initial data. We combine the conformal method applied to a background perfect fluid theory with a perturbative argument in order to obtain the result.
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- PAR ID:
- 10588306
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Mathematical Physics
- Volume:
- 65
- Issue:
- 12
- ISSN:
- 0022-2488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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