This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rd, where d = 2, 3, with initial data B0∈ Hs(Rd) and u0∈ Hs - 1 + ϵ(Rd) for s> d/ 2 and any 0 < ϵ< 1. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking ϵ= 0 is explained by the failure of solutions of the heat equation with initial data u0∈ Hs - 1 to satisfy u∈ L1(0 , T; Hs + 1) ; we provide an explicit example of this phenomenon.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering