Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent (Q2121080)

It is well-known that the hyperdissipative Navier-Stokes equations (with a fractional \(\alpha\)-power of Laplacian replacing the usual dissipation term) in three-dimensional case have unique solutions when \(\alpha>5/4\). The case of stochastic Navier-Stokes equations is discussed on three-diemnsional torus. Nonuniqueness of solutions in law is shown when \(\alpha<5/4\).