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arXiv · 1505.07214

Wellposedness for density-dependent incompressible viscous fluids on the torus $\T^3$

Eugénie Poulon
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Abstract

We investigate the local wellposedness of incompressible inhomogeneous Navier-Stokes equations on the Torus $\T^3$, with initial data in the critical Besov spaces. Under some smallness assumption on the velocity in the critical space $B^{\frac{1}{2}}\_{2,1}(\T^3)$, the global-in-time existence of the solution is proved. The initial density is required to belong to~$B^{\frac{3}{2}}\_{2,1}(\T^3)$ but not supposed to be small.

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Eugénie Poulon. 2015-05-27. Wellposedness for density-dependent incompressible viscous fluids on the torus $\T^3$. https://arxiv.org/abs/1505.07214

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