The optimal decay rates of classical solutions to the 3D compressible Navier‐Stokes equations. Issue 10 (28th April 2021)

• Record Type: Journal Article
• Authors: Xu, Fuyi; Chi, Meiling; Jiang, Jiqiang; Cui, Yujun
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 101:Issue 10(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-04-28
• Subjects: Besov spaces -- compressible Navier‐Stokes equations -- optimal decay rates; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201900113
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: In this paper, we revisit the optimal time decay rates of classical solutions to the 3D compressible Navier‐Stokes equations. Based on a global priori estimate, the optimal time decay rates of the solution and its first order derivative in L 2 ‐norm are obtained if H l ‐norm ( l ≥ 4 ) of the initial perturbation around a constant state is small enough and ∥ ( ρ 0 − ρ ¯, m 0 ) ∥ B ̇ 1, ∞ − s ℓ is bounded for s ∈ [ 0, 1 2 ) . Compared with the previous works by Hai‐Liang Li and Ting Zhang (Math Meth Appl Sci 34:670‐682, 2011), we remove the smallness of ∥ ( ρ 0 − ρ ¯, m 0 ) ∥ B ̇ 1, ∞ − s and our condition involves only the low frequencies of the data in B ̇ 1, ∞ − s ( R 3 ) . Abstract : In this paper, we revisit the optimal time decay rates of classical solutions to the 3D compressible Navier‐Stokes equations. Based on a global priori estimate, the optimal time decay rates of the solution and its first order derivative in L 2 ‐norm are obtained if H l ‐norm ( l ≥ 4 ) of the initial perturbation around a constant state is small enough and ∥ ( ρ 0 − ρ ¯, m 0 ) ∥ B ̇ 1, ∞ − s ℓ is bounded for s ∈ [ 0, 1 2 ) . Compared with the previous works by Hai‐Liang Li and Ting Zhang (Math Meth Appl Sci 34:670‐682, 2011), we remove the smallness of ∥ ( ρ 0 − ρ ¯, m 0 ) ∥ B ̇ 1, ∞ − s and our condition involves only the low frequencies of the data in B ̇ 1, ∞ − s ( R 3 ) .