TY - JOUR
T1 - Interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations
AU - Kang, Kyungkeun
AU - Lee, Jihoon
PY - 2009/10/15
Y1 - 2009/10/15
N2 - We present new interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations in dimension three: a suitable weak solution is regular near an interior point z if the scaled Lx, tp, q-norm of the velocity with 1 ≤ 3 / p + 2 / q ≤ 2, 1 ≤ q ≤ ∞ is sufficiently small near z and if the scaled Lx, tl, m-norm of the magnetic field with 1 ≤ 3 / l + 2 / m ≤ 2, 1 ≤ m ≤ ∞ is bounded near z. Similar results are also obtained for the vorticity and for the gradient of the vorticity. Furthermore, with the aid of the regularity criteria, we exhibit some regularity conditions involving pressure for weak solutions of the magnetohydrodynamic equations.
AB - We present new interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations in dimension three: a suitable weak solution is regular near an interior point z if the scaled Lx, tp, q-norm of the velocity with 1 ≤ 3 / p + 2 / q ≤ 2, 1 ≤ q ≤ ∞ is sufficiently small near z and if the scaled Lx, tl, m-norm of the magnetic field with 1 ≤ 3 / l + 2 / m ≤ 2, 1 ≤ m ≤ ∞ is bounded near z. Similar results are also obtained for the vorticity and for the gradient of the vorticity. Furthermore, with the aid of the regularity criteria, we exhibit some regularity conditions involving pressure for weak solutions of the magnetohydrodynamic equations.
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U2 - 10.1016/j.jde.2009.07.016
DO - 10.1016/j.jde.2009.07.016
M3 - Article
AN - SCOPUS:68949146842
SN - 0022-0396
VL - 247
SP - 2310
EP - 2330
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 8
ER -