Large-bulk-viscosity limit for two-dimensional compressible micropolar fluids with vacuum

We consider the Cauchy problem for the two-dimensional compressible micropolar fluid system on the torus T². The initial density is bounded and nonnegative and may contain vacuum, while the initial velocity and microrotation belong to H¹( T²). For sufficiently large bulk viscosity $ν$, we prove the global-in-time existence of solutions without a smallness assumption on the H¹ size of the data, provided that the initial compressible component is well prepared in the sense that √ν\|divu₀\|L² is uniformly bounded. The proof combines the effective viscous flux with a coupled energy scheme that exploits the vorticity--microrotation dissipation at both the basic and material-derivative levels. For the linear pressure law, we also prove uniqueness in the stated solution class by means of a coupled backward parabolic problem, logarithmic interpolation, and Osgood's lemma. For fixed initial data with divu₀=0, we also justify the limit ν→∞: every sequence of the corresponding solutions admits a subsequence converging to a solution of the two-dimensional inhomogeneous incompressible micropolar system.