Abstract: 

This talk concerns the time growth of the highest-order energy of the systems of two dimensional incompressible isotropic Hookean elastodynamics. This two dimensional system is nonlocal quasilinear wave equations where the unknowns has slow temporal decay. By observing an inherent strong null structure, the global well-posedness of smooth solutions near equilibrium was first proved by Lei where the highest-order generalized energy may have certain growth in time. We improve the result and show that the highest-order generalized energy is uniformly bounded for all the time.

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