# 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} }

- Published 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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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 64 REFERENCES

## Symmetries and Critical Phenomena in Fluids

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## The growth of the vorticity gradient for the two-dimensional Euler flows on domains with corners

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Potentially singular solutions of the 3D axisymmetric Euler equations.

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## On the Effects of Advection and Vortex Stretching

VIEW 1 EXCERPT

## Remarks on functions with bounded Laplacian

VIEW 2 EXCERPTS

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