Equatorial wind waves with capillary effects and stagnation points

We consider here waves that propagate in equatorial oceanic regions. By means of Crandall–Rabinowitz bifurcation theory we prove existence of steady periodic two-dimensional equatorial geophysical water waves with capillary effects and stagnation points. We also show that if the vorticity is big enough these flows possess stagnation points. Moreover, we prove that the free surface has a priori regularity. The dispersion relation, i.e. a formula giving the speed at the free surface of the bifurcating laminar flow (in terms of the constant vorticity, mean depth, wave number, Earth’s rotation speed), is also provided.