Global classical solutions of 3D compressible viscoelastic system near equilibrium

In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde ρ_0 \det F_0 =1$) and the "div-curl" structure assumption compared with previous works. It then broadens the class of solutions to a great extent, more precisely the initial density state would not be constant necessarily, and no more structure is need for global well-posedness. It's quite different from the elasticity system in which structure plays an important role. Since we can not obtain any dissipation information for density and deformation tensor, we introduce a new effective flux in the thought of regarding the wildest "nonlinear term" as "linear term". Although the norms of solution may increase now, we can still derive the global existence for it.

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