Finite-time Singularity Formation for Strong Solutions to the Boussinesq System

@inproceedings{Elgindi2017FinitetimeSF,
  title={Finite-time Singularity Formation for Strong Solutions to the Boussinesq System},
  author={T. M. Elgindi and In-Jee Jeong},
  year={2017}
}
The global regularity problem for the Boussinesq system is a well known open problem in mathematical fluid dynamics. As a follow up to our work \cite{EJSI}, we give examples of finite-energy and Lipschitz continuous velocity field and density $(u_0,\rho_0)$ which are $C^\infty$-smooth away from the origin and belong to a natural local well-posedness class for the Boussinesq equation whose corresponding local solution becomes singular in finite time. That is, while the sup norm of the gradient… CONTINUE READING

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