This paper addresses several problems associated to local energy solutions (in the sense of
Lemarié-Rieusset) to the Navier-Stokes equations with initial data which is sufficiently small …

We introduce a notion of global weak solution to the Navier–Stokes equations in three
dimensions with initial values in the critical homogeneous Besov spaces ̇ B^-1+ 3 p _ p, ∞ …

We obtain a global existence result for the three-dimensional Navier-Stokes equations with
a large class of data allowing growth at spatial infinity. Namely, we show the global …

We prove short time regularity of suitable weak solutions of 3D incompressible Navier–
Stokes equations near a point where the initial data is locally in. The result is applied to the …

Chae and Wolf recently constructed discretely self-similar solutions to the Navier–Stokes
equations for any discretely self-similar data in L loc 2. Their solutions are in the class of …

We are concerned with the size of the regular set for weak solutions to the Navier–Stokes
equations. It is shown that if a weighted L 2 norm of initial data is finite, the suitable weak …

Discretely self-similar solutions to Oberbeck-Boussinesq system with Newtonian
gravitational field for large discretely self-similar initial data are constructed in this note …

We prove an $\epsilon $-regularity criterion for the 3D Navier-Stokes equations in terms of
initial data. It shows that if a scaled local $ L^ 2$ norm of initial data is sufficiently small …

Forward self-similar and discretely self-similar weak solutions of the Navier–Stokes
equations are known to exist globally in time for large self-similar and discretely self-similar …

We construct self-similar solutions to the three dimensional Navier–Stokes equations for
divergence free, self-similar initial data that can be large in the critical Besov space ̇ B _ p …