In his thesis he showed that in a dense fluid the interactions are different from what they are at equilibrium and propagate through hydrodynamic modes, which leads to the divergence of transport coefficients in 2 spatial dimensions. This aroused his interest in fluid mechanics, and in the transition to turbulence. Together with Paul Manneville, Yves Pomeau discovered a new mode of transition to turbulence, the transition by temporal
Intermittency, which was confirmed by numerous
experimental observations and
CFD simulations. This is the so-called
Pomeau–Manneville scenario, associated with the
Pomeau-Manneville maps In papers published in 1973 and 1976, Jean Hardy, Yves Pomeau and Olivier de Pazzis introduced
the first lattice Boltzmann model, which is called the
HPP model after the authors. Generalizing ideas from his thesis, together with
Uriel Frisch and
Brosl Hasslacher, Yves Pomeau found a very simplified microscopic fluid model (FHP model) which allows simulating very efficiently the complex movements of a real fluid. He was a pioneer of
lattice Boltzmann methods and played a historical role in the
timeline of computational physics. Reflecting on the situation of the transition to turbulence in parallel flows, he showed that turbulence is caused by a contagion mechanism, and not by local instability.
Front can be static or mobile depending on the conditions of the system, and the causes of the motion can be the variation of a free energy, where the most energetically favorable state invades the less favorable one. The consequence is that this transition belongs to the class of directed percolation phenomena in statistical physics, which has also been amply confirmed by experimental and numerical studies. In dynamical systems theory, the structure and length of the attractors of a network corresponds to the dynamic phase of the network.
The stability of Boolean network depends on the connections of their nodes. A Boolean network can exhibit stable, critical or chaotic behavior. This phenomenon is governed by a critical value of the average number of connections of nodes (K_{c}), and can be characterized by the Hamming distance as distance measure. If p_{i}=p=const. for every node, the transition between the stable and chaotic range depends on p .
Bernard Derrida and Yves Pomeau proved that, the critical value of the average number of connections is K_{c}=1/[2p(1-p)] . A droplet of nonwetting viscous liquid moves on an inclined plane by rolling along it. Together with
Lakshminarayanan Mahadevan, he gave a scaling law for the uniform speed of such a droplet. With Christiane Normand, and
Manuel García Velarde, Yves Pomeau studied convective instability. Apart from simple situations, capillarity remains an area where fundamental questions remain. He showed that the discrepancies appearing in the hydrodynamics of the moving contact line on a solid surface could only be eliminated by taking into account the evaporation/condensation near this line. Capillary forces are almost always insignificant in solid mechanics. Nevertheless, with Serge Mora, Ty Phou, Jean-Marc Fromental and Len M. Pismen they have shown theoretically and experimentally that soft gel filaments are subject to Rayleigh-Plateau instability, an instability never observed before for a solid. In collaboration with his former PhD student
Basile Audoly and
Henri Berestycki, he studied the speed of the propagation of a reaction front in a fast steady flow with a given structure in space. With
Basile Audoly and Martine Ben Amar, Pomeau developed a theory of large deformations of elastic plates which led them to introduce the concept of "
d-cone", that is, a geometrical cone preserving the overall developability of the surface, an idea now taken up by the solid mechanics community. The theory of superconductivity is based on the idea of the formation of pairs of electrons that become more or less bosons undergoing Bose-Einstein condensation. This pair formation would explain the halving of the flux quantum in a superconducting loop. Together with Len Pismen and Sergio Rica they have shown that, going back to Onsager's idea explaining the quantification of the circulation in fundamental quantum states, it is not necessary to use the notion of electron pairs to understand this halving of the circulation quantum. He also analyzed the onset of BEC from the point of view of kinetic theory. Whereas the kinetic equation for a dilute Bose gas had been known for many years, the way it can describe what happens when the gas is cooled down to reach temperature below the temperature of transition. At this temperature the gas gets a macroscopic component in the quantum ground state, as had been predicted by Einstein long ago. Together with Christophe Josserand and Sergio Rica, Pomeau showed that the solution of the kinetic equation becomes singular at zero energies and we did also find how the density of the condensate grows with time after the transition. Marc-Étienne Brachet, Stéphane Métens, Sergio Rica and Yves Pomeau also derived the kinetic equation for the Bogoliubov excitations of Bose-Einstein condensates, where Yves Pomeau and Minh-Binh Tran found three collisional processes. Before the surge of interest in super-solids started by Moses Chan experiments, Sergio Rica and Yves Pomeau had shown in an early simulation that a slightly modified NLS equation yields a fair representation of super-solids. With
Alan C. Newell, he studied turbulent crystals in macroscopic systems. From his more recent work we must distinguish those concerning a phenomenon typically out of equilibrium, that of the emission of photons by an atom maintained in an excited state by an intense field that creates Rabi oscillations. The theory of this phenomenon requires a precise consideration of the statistical concepts of quantum mechanics in a theory satisfying the fundamental constraints of such a theory. With Martine Le Berre and
Jean Ginibre, Yves Pomeau showed that the good theory was that of a Kolmogorov equation based on the existence of a small parameter, the ratio of the photon emission rate to the atomic frequency itself. ==Known for==