TY - JOUR
T1 - Remarks on the non-uniqueness in law of the Navier–Stokes equations up to the J.-L. Lions’ exponent
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/5
Y1 - 2022/5
N2 - Lions (1959), introduced the Navier–Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the uniqueness of its solution when its exponent is not less than five quarters in case the spatial dimension is three. Following the work of Hofmanová et al. (2019), we prove the non-uniqueness in law for the three-dimensional stochastic Navier–Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.
AB - Lions (1959), introduced the Navier–Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the uniqueness of its solution when its exponent is not less than five quarters in case the spatial dimension is three. Following the work of Hofmanová et al. (2019), we prove the non-uniqueness in law for the three-dimensional stochastic Navier–Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.
KW - Convex integration
KW - Fractional Laplacian
KW - Navier–Stokes equations
KW - Non-uniqueness
KW - Random noise
UR - http://www.scopus.com/inward/record.url?scp=85124322016&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2022.01.016
DO - 10.1016/j.spa.2022.01.016
M3 - Article
AN - SCOPUS:85124322016
SN - 0304-4149
VL - 147
SP - 226
EP - 269
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -