Decay property of regularity-loss type for the Euler–Cattaneo–Maxwell system

Kawashima and Ueda [Mathematical entropy and Euler–Cattaneo–Maxwell system. Anal Appl. 2016:14:101–143] first proposed Euler–Cattaneo–Maxwell system which satisfies classical thermodynamics by using Cattaneo law. Furthermore, they got the global existence and asymptotic stability of solutions to the system. Our work is dedicated to solving the decay property of the Euler–Cattaneo–Maxwell system in R3. Under the assumption of s≥6, we obtain that the global solution of the system decays at the rate t−3/4 when t→∞, if the initial data in Hs∩L1 has enough regularity. Our main method relies on time-weighted energy method with some special matrices.