Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
نویسندگان
چکیده
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in R , where d = 2, 3, with initial data B0 ∈ H (R) and u0 ∈ H s−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 ∈ H s−1 to satisfy u ∈ L(0, T ; H s+1); we provide an explicit example of this phenomenon.
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