TY - JOUR
T1 - Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces
AU - Fefferman, Charles L.
AU - McCormick, David S.
AU - Robinson, James C.
AU - Rodrigo, Jose L.
N1 - Publisher Copyright:
© 2016, The Author(s).
PY - 2017/2/1
Y1 - 2017/2/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00205-016-1042-7
DO - 10.1007/s00205-016-1042-7
M3 - Article
AN - SCOPUS:84984830306
SN - 0003-9527
VL - 223
SP - 677
EP - 691
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -