Long-time existence of nonlinear inhomogeneous compressible elastic waves
Abstract
In this paper, we consider the nonlinear inhomogeneous compressible elastic waves in three spatial dimensions when the density is a small disturbance around a constant state. In homogeneous case, the almost global existence was established by Klainerman-Sideris [1996CPAM], and global existence was built by Agemi [2000Invent. Math.] and Sideris [1996Invent. Math., 2000Ann. Math.] independently. Here we establish the corresponding almost global and global existence theory in the inhomogeneous case.
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