Global strong solutions for the multi-dimensional compressible viscoelastic flows with general pressure law

In this paper, we mainly focus on the compressible viscoelastic flows of Oldroyd type with general pressure law, one non-Newtonian fluids exhibiting elastic behavior. For P′(ρ̄)+α>0, α > 0 being elasticity coefficient fluid, prove global existence and uniqueness strong solution in critical Besov spaces when initial data u⃗0 low frequency part ρ0, τ0 are small enough compared to viscosity coefficients. particular, is large, can be large. The proof display here does not need any compatible conditions. addition, also obtain optimal decay rates spaces.