Hervé Le Meur
Small-time existence for a viscoelastic model with free bounday and a free surface.
prove the small-time existence of the solution of a
Johnson-Segalmann-type viscoelastic fluid for any initial data and a
free boundary. We take into account the surface tension.
purpose, we split the Navier-Stokes part of the equations, which is
solved in G. Allain Appl. Math. Optim. 16 (1987), no.
1, 37--50, and the purely viscoelastic constitutive equation. In the
Lagrangian coordinates, the constitutive equation improves the time
regularity. This enables to have continuity constants depending on the
final time in a convenient way. Then we estimate all the error terms
and then prove the result with a fixed point theorem.