Abstract
We consider the long-time behavior and optimal decay rates of global strong solutions for the isentropic compressible Euler equations with damping in R 3 in the present paper. When the regular initial data belong to some Sobolev space H l ( R 3 ) ∩ B ˙ 1 , ∞ − s ( R 3 ) with l ⩾ 4 and s ∈ [ 0 , 1 ] , we show that the density of the system converges to its equilibrium state at the rates ( 1 + t ) − 3 4 − s 2 in the L 2 -norm or ( 1 + t ) − 3 2 − s 2 in the L ∞ -norm respectively; the momentum of the system decays at the rates ( 1 + t ) − 5 4 − s 2 in the L 2 -norm or ( 1 + t ) − 2 − s 2 in the L ∞ -norm respectively, which are shown to be optimal for the compressible Euler equations with damping.
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