an:06705720
Zbl 1366.35126
Danchin, Rapha??l; Xu, Jiang
Optimal time-decay estimates for the compressible Navier-Stokes equations in the critical \(L^{p}\) framework
EN
Arch. Ration. Mech. Anal. 224, No. 1, 53-90 (2017).
00363737
2017
j
35Q35 76N10 35B40 35B65
compressible Navier-Stokes system; decay estimates; critical spaces
This work is devoted to the derivation of the (optimal) time decay rates of solutions for the isentropic compressible Navier-Stokes equations in the norms of critical spaces. The existence of global in time solutions has been discussed previously in \(L^2\) [\textit{R. Danchin}, Invent. Math. 141, No. 3, 579--614 (2000; Zbl 0958.35100)] and \(L^p\) frameworks [\textit{F. Charve} and \textit{R. Danchin}, Arch. Ration. Mech. Anal. 198, No. 1, 233--271 (2010; Zbl 1229.35167)], [\textit{Q. Chen} et al., Commun. Pure Appl. Math. 63, No. 9, 1173--1224 (2010; Zbl 1202.35002)], [\textit{B. Haspot}, Arch. Ration. Mech. Anal. 202, No. 2, 427--460 (2011; Zbl 1427.76230)]. The method of proof relies on refined time weighted inequalities in the Fourier space.
Piotr Biler (Wroc??aw)
Zbl 0958.35100; Zbl 1229.35167; Zbl 1202.35002; Zbl 1427.76230