Well-posedness for the motion of an incompressible liquid with free surface boundary

• Autores: Hans Lindblad
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 1, 2005, págs. 109-194
• Idioma: inglés
• DOI: 10.4007/annals.2005.162.109
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• Resumen

  • We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler¿s equations, where the regularity of the boundary enters to highest order. We prove local existence in Sobolev spaces assuming a ¿physical condition¿, related to the fact that the pressure of a fluid has to be positive.