Instantaneous gelation and nonexistence for the Oort-Hulst-Safronov coagulation model
Pooja Rai, Ankik Kumar Giri, Volker John
TL;DR
This paper investigates the phenomenon of instantaneous gelation in the Oort-Hulst-Safronov coagulation model, demonstrating that for certain kernels, solutions do not exist at any time, indicating nonexistence of mass conservation.
Contribution
It proves the nonexistence of solutions and the occurrence of instantaneous gelation for specific unbounded kernels in the OHS coagulation model.
Findings
Instantaneous gelation occurs for certain kernels.
No mass-conserving weak solutions exist for these kernels.
Solutions do not exist at any time for the studied kernels.
Abstract
The possible occurrence of instantaneous gelation to Oort-Hulst-Safronov (OHS) coagulation equation is investigated for a certain class of unbounded coagulation kernels. The existence of instantaneous gelation is confirmed by showing the nonexistence of mass-conserving weak solutions. Finally, it is shown that for such kernels, there is no weak solution to the OHS coagulation equation at any time interval.
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Taxonomy
TopicsNavier-Stokes equation solutions · Nonlinear Partial Differential Equations