Uniform bound of the highest-order energy for three dimensional inhomogeneous incompressible elastodynamics

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Abstract

We are concerned with the time growth of the highest-order energy of three-dimensional inhomogeneous incompressible isotropic elastodynamics. Utilizing Klainerman’s generalized energy method, refined weighted estimates, and the Keel-Smith-Sogge estimate [J. Anal. Math., 87: 265–279, 2002], it is justified that the highest-order generalized energy is uniformly bounded for all time.

Keywords

inhomogeneous incompressible elastodynamics / uniform bound / highest-order energy / KSS estimate / vector field theory

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