This talk will focus on the compressible dissipative elastodynamic system with zero shear viscosity in 2D. The global stability around a constant equilibrium is given. Due to the low pointwise dispersive estimate for the divergence-free projection of solutions, and the lack of null structures in convective terms, energy estimates, combined with Green's functions and dispersive estimates, for both solutions and their potentials are obtained to control the interactions in nonlinear terms. This is a joint work with Prof. Xianpeng Hu (CityU).

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