Dissipative structure of some viscous-dispersive systems in compressible fluid dynamics

par José Valdovinos

mardi 3 févr. 2026, 11:00 → 12:15 Europe/Paris

In this talk I will start by presenting Humpherys's equivalence theorem for linear high-order systems, which is a generalization of the classical equivalence theorem by Shizuta and Kawashima for second order systems. The theorem states the equivalence between the strict dissipativity and genuine coupling conditions, and the existence of a compensating matrix function for the system. Next, I will present a result that describes the dissipative structure of these high order-systems, and apply it to some systems in compressible fluid dynamics: the Navier-Stokes-Fourier-Korteweg model; the Euler-Fourier-Korteweg system; and a dispersive Navier-Stokes-Fourier system proposed by Levermore and Sun. Finally, for the NSFK system I will explain how the linear results can be used to obtain decay rates for small perturbations of constants states for the nonlinear system. The results are part of joint works with Angeles, F. and Plaza, R.G..