Pressure behavior and wave height estimates for steady periodic equatorial water waves

In the present paper, we investigate steady two-dimensional periodic equatorial water waves propagating at the surface of water above a flat bed. Under certain conditions, we present some behavior of the pressure and one of the dynamic pressure, respectively. Furthermore, we derive some lower bounds of wave heights in the irrotational setting, which lean on the pressure (or dynamic pressure) data at the random intermediate depth. Moreover, upper bounds of wave heights for the case of small non-positive vorticity are obtained, which are associated with the velocity and pressure measurements at an random intermediate depth.