Constantin specializes in the role of mathematics in geophysics using nonlinear partial differential equations to mathematically model currents and waves in the oceans and in the atmosphere. These flows and waves play an important role in the El Niño climate phenomenon and in natural disasters such as tsunamis.[6] His approach takes into account the fact that the surface of the earth is curved[7] and the importance of the Coriolis force.[2][8]
2000: Stability of peakons (with W. Strauss), Comm. Pure Appl. Math. 53 603–610.
2004: Exact steady periodic water waves with vorticity (with W. Strauss), Comm. Pure Appl. Math. 57 481–527.
2006: The trajectories of particles in Stokes waves, Invent. Math. 166 523–535.
2007: Global conservative solutions of the Camassa-Holm equation (with A. Bressan), Arch. Ration. Mech. Anal. 183 215–239.
2011: Analyticity of periodic traveling free surface water waves with vorticity (with J. Escher), Ann. of Math. 173 559–568.
2016: Global bifurcation of steady gravity water waves with critical layers (with W. Strauss and E. Varvaruca), Acta Mathematica 217 195–262.
2019: Equatorial wave-current interactions (with R. I. Ivanov), Comm. Math. Phys. 370 1–48.
2022: On the propagation of nonlinear waves in the atmosphere (with R. S. Johnson), Proceedings of the Royal Society A 478 (2260), 20210895
2022: Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere (with P. Germain), Arch. Ration. Mech. Anal., (245 587–644)