128 citations · 227 across the 8 of their papers we have counts for
6 papers · 1 filter
Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
Charles L. Fefferman, David S. McCormick, James C. Robinson +1
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in , , with i…
Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in , , and
David S. McCormick, Eric J. Olson, James C. Robinson +3
If is a smooth solution of the Navier--Stokes equations on with first blowup time , we prove lower bounds for in the Sobolev spaces , $\dot…
Local existence for the non-resistive MHD equations in Besov spaces
Jean-Yves Chemin, David S. McCormick, James C. Robinson +1
In this paper we prove the existence of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations on the whole of , , for divergence-free…
Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
C. L. Fefferman, D. S. McCormick, J. C. Robinson +1
This paper establishes the local-in-time existence and uniqueness of strong solutions in for to the viscous, non-resistive magnetohydrodynamics (MHD) equations in…
Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation
David S. McCormick, James C. Robinson, Jose L. Rodrigo
We prove existence, uniqueness and regularity of weak solutions of a coupled parabolic-elliptic model in two dimensions; we consider the standard equations of magnetohydrodynamics…
Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO
David S. McCormick, James C. Robinson, Jose L. Rodrigo
Using elementary arguments based on the Fourier transform we prove that for and with , if $f \in L^{q,\infty}(\R^n) \cap \dot{H}^…