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arXiv · 1708.05666

Ill-posedness of Leray solutions for the ipodissipative Navier-Stokes equations

Maria Colombo·Camillo De Lellis·Luigi De Rosa
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Abstract

We prove the ill-posedness of Leray solutions to the Cauchy problem for the ipodissipative Navier--Stokes equations, when the dissipative term is a fractional Laplacian $(-Δ)^α$ with exponent $α< \frac{1}{5}$. The proof follows the ''convex integration methods'' introduced by the second author and László Székelyhidi Jr. for the incomprresible Euler equations. The methods yield indeed some conclusions even for exponents in the range $[\frac{1}{5}, \frac{1}{2}[$.

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Maria Colombo, Camillo De Lellis, Luigi De Rosa. 2017-08-17. Ill-posedness of Leray solutions for the ipodissipative Navier-Stokes equations. https://doi.org/10.1007/s00220-018-3177-x

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