an:01753081
Zbl 1028.35126
Toland, J. F.
On a pseudo-differential equation for Stokes waves
EN
Arch. Ration. Mech. Anal. 162, No. 2, 179-189 (2002).
00084472
2002
j
35Q35 35S05 35R35 76B15
nonlinear pseudodifferential equation; conformal mapping; nonlinear elliptic free-boundary problem for Stokes waves
Author's summary: It is shown that the existence of a smooth solution to a nonlinear pseudodifferential equation on the unit circle is equivalent to the existence of a globally injective conformal mapping in the complex plane which gives a smooth solution to the nonlinear elliptic free-boundary problem for Stokes waves in hydrodynamics.
A dual formulation is used to show that the equation has no non-trivial smooth solutions, stable or otherwise, that would correspond to a Stokes wave with gravity acting in a direction opposite to that which is physically realistic.
P.Godin (Bruxelles)