Extrema of the dynamic pressure in an irrotational Stokes wave with underlying currents and infinite depth

In this paper, we investigate the dynamic pressure in an irrotational Stokes wave in flows of finite depth with uniform underlying currents and infinite depth without underlying currents respectively. Using the maximum principles in combination with exploiting some of the physical structures of the problem itself, we prove that, irrespectively of uniform underlying current, infinite depth and wave amplitude, the maximum and minimum of the dynamic pressure are attained at the wave crest and at the wave trough respectively.