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Forward discretely self-similar solutions of the Navier-Stokes equations II (1510.07504v1)
Published 26 Oct 2015 in math.AP
Abstract: For any discretely self-similar, incompressible initial data $v_0$ which satisfies $|v_0 |_{L3_w(\mathbb R3)}\leq c_0$ where $c_0$ is allowed to be large, we construct a forward discretely self-similar local Leray solution in the sense of Lemari\'e-Rieusset to the 3D Navier-Stokes equations in the whole space. No further assumptions are imposed on the initial data; in particular, the data is not required to be continuous or locally bounded on $\mathbb R3\setminus {0}$. The same method is used to construct self-similar solutions for any $-1$-homogeneous initial data in $L3_w$.