Abstract
We study the global-in-time well-posedness and relaxation limit of the compressible Euler system with damping in L p L^p -type critical Besov spaces. In comparison with the results obtained by Crin-Barat and Danchin [Pure Appl. Anal. 4 (2022), pp. 85â125; Math. Ann. 386 (2023), pp. 2159â2206], the more general pressure law satisfying P âČ ( Ï ÂŻ ) > 0 Pâ(\bar {\rho })>0 is allowed. To achieve it, a new composition estimate is established in the L 2 L^2 - L p L^p hybrid Besov spaces with explicit dependence on the threshold between high frequencies and low frequencies.
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