Infinite energy solutions for damped Navier-Stokes equations in \({\mathbb{R}^2}\) (Q2441520)

This paper consider the damped Navier-Stokes equations in the whole \({\mathbb{R}^2}\). The global well-posedness, dissipativity and further regularity are studied in the uniformly-local spaces under the assumption that the given initial velocity \({u_0 \in L^\infty(\mathbb{R}^2)}\). Further, as an application, it is shown that the properly defined weak solution to the classical Navier-Stokes equation in \({\mathbb{R}^2}\) can grow at most polynomially as time goes to infinity.