Two-dimensional incompressible micropolar fluid models with singular initial data Béjar López, Alexis Cunha, Cleyton Soler, Juan Fluid dynamics Micropolar fluids NonNewtonian fluids Singular vorticity Morrey spaces Navier–Stokes This paper was carried out in part during Cleyton Cunha’s visit to the Department of Applied Mathematics of the University of Granada from November 2019 to August 2020. Cleyton Cunha thanks the Omar Guzmán for discussions about this work and for his critical reading of the manuscript. This work has been partially supported by the MINECO-Feder (Spain) research grant number RTI2018-098850-B-I00, the Junta de Andalucía (Spain) Project PY18-RT-2422, B-FQM-580-UGR20 & A-FQM-311- UGR18 and by the CAPES/PRINT (Brazil) - Finance Code 001, #8881.311964/2018-01 (CC) and the MECD (Spain) research grant FPU19/01702 (AB-L). Funding for open access charge: Universidad de Granada / CBUA. This paper deals with the interaction between microstructures and the appearance or persistence of singular configurations in the Cauchy problem for the two-dimensional model of incompressible micropolar fluids. We analyze the case of null angular viscosity and singular initial data, including the possibility of vortex sheets or measures as initial data in Morrey spaces. Through integral techniques we establish the existence of weak solutions local or global in time. In addition, the uniqueness and stability of these solutions is analyzed. 2022-01-10T13:39:05Z 2022-01-10T13:39:05Z 2022-02 journal article A. Béjar-López, C. Cunha and J. Soler. Two-dimensional incompressible micropolar fluid models with singular initial data. Physica D 430 (2022) 133069. [https://doi.org/10.1016/j.physd.2021.133069] http://hdl.handle.net/10481/72284 10.1016/j.physd.2021.133069 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España Elsevier