The uniqueness of nondecaying solutions for the Navier-Stokes equations (Q1417408)

The author considers an initial value problem for Navier-Stokes equations in the whole space \({\mathbb R}^{n}\). He proves the uniqueness of solutions under the assumptions that the velocity field is bounded, and the pressure field is a locally integrable-in-time function of bounded mean oscillations for bounded initial data. In this case the velocity field may not decay at space infinity. Although there are various results concerning uniqueness without the decay assumption, the presented result is new and applicable to solutions constructed by solving the integral equations.