Title Ill-posedness of Leray solutions for the ipodissipative Navier–Stokes equations Publication Type Journal Article Year of Publication 2018 Authors Colombo M., De Lellis C., De Rosa L. Journal Communications in Mathematical Physics Volume 362 Issue 2 Pagination 659–688 Date Published September Publisher Springer Type of Article NS ISSN 0010-3616 Keywords Mathematical Physics, Statistical and Nonlinear Physics Abstract We prove the ill-posedness of Leray solutions to the Cauchy problem for the hypodissipative Navier?Stokes equations and when the dissipative term is a fractional Laplacian \$(?\ensuremathΔ)\^ \ensuremathα\$ with exponent \$\ensuremathα\ensuremath<$\backslash$frac{1}{5}\$. The proof follows the ?convex integration methods? introduced by the second author and László Székelyhidi Jr. for the incompressible Euler equations. The methods yield indeed some conclusions even for exponents in the range \$[$\backslash$frac{1}{5},$\backslash$frac{1}{2}[\$. Notes Comm. Math. Phys. 362 (2018) no. 2, 659-688 URL https://link.springer.com/article/10.1007/s00220-018-3177-x DOI 10.1007/s00220-018-3177-x
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