Mass-conserving weak solutions to Oort-Hulst-Safronov coagulation equation with singular rates

Existence of global weak solutions to the continuous Oort-Hulst-Safronov (OHS) coagulation equation is investigated for coagulation kernels capturing a singularity near zero and growing linearly at infinity. The proof mainly relies on a relation, between classical Smoluchowski coagulation equation (SCE) and OHS coagulation equation, which is introduced in [16] as generalized coagulation equation. Moreover, all weak solutions formulated in a suitable sense are demonstrated to be mass-conserving. We obtain here a similar result for OHS coagulation equation as the one in [6] for SCE.