Iooss's research deals with functional analysis of the Navier-Stokes equation, nonlinear hydrodynamic stability theory and water waves of different kinds, and general behavior (such as symmetry breaking and normal forms) of bifurcations (branching of solutions) in dynamic systems. In 1971, independently of David H. Sattinger, he treated the Hopf bifurcation in solutions of the Navier-Stokes equation as an infinite dimensional dynamical system. He studied in particular the Couette flow (Taylor-Couette) and discovered there theoretically several waveforms, which were later confirmed experimentally. He collaborated with Alain Chenciner on bifurcation of invariant tori. Iooss, with Pierre Coullet, classified the instabilities of spatially periodic patterns in translation-invariant and mirror-symmetric systems.
