Publication Date:
2020-06-12
Description:
This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the $$H^{4}imes H^{3}$$ H 4 × H 3 framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in $$L^2$$ L 2 -norm is $$(1+t)^{-frac{3}{4}}$$ ( 1 + t ) - 3 4 if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the $$k(kin [1, 3])$$ k ( k ∈ [ 1 , 3 ] ) th-order spatial derivatives of solution converging to zero in $$L^2$$ L 2 -norm is $$(1+t)^{-frac{3+2k}{4}}$$ ( 1 + t ) - 3 + 2 k 4 . Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in $$L^2$$ L 2 -norm is $$(1+t)^{-frac{5}{4}}$$ ( 1 + t ) - 5 4 .
Print ISSN:
0044-2275
Electronic ISSN:
1420-9039
Topics:
Mathematics
,
Physics
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