TY - JOUR
T1 - Hölder continuity for a drift-diffusion equation with pressure
AU - Silvestre, Luis
AU - Vicol, Vlad
N1 - Funding Information:
Luis Silvestre was partially supported by NSF grant DMS-1001629 and the Sloan Foundation. Vlad Vicol was partially supported by an AMS-Simmons travel grant.
PY - 2012
Y1 - 2012
N2 - We address the persistence of Hölder continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressureu t+b·∇ u-Δu=∇p, Δu=0 on [0,∞) × ℝn, with n≥2. The drift velocity b is assumed to be at the critical regularity level, with respect to the natural scaling of the equations. The proof draws on Campanato's characterization of Hölder spaces, and uses a maximum-principle-type argument by which we control the growth in time of certain local averages of u. We provide an estimate that does not depend on any local smallness condition on the vector field b, but only on scale invariant quantities.
AB - We address the persistence of Hölder continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressureu t+b·∇ u-Δu=∇p, Δu=0 on [0,∞) × ℝn, with n≥2. The drift velocity b is assumed to be at the critical regularity level, with respect to the natural scaling of the equations. The proof draws on Campanato's characterization of Hölder spaces, and uses a maximum-principle-type argument by which we control the growth in time of certain local averages of u. We provide an estimate that does not depend on any local smallness condition on the vector field b, but only on scale invariant quantities.
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U2 - 10.1016/j.anihpc.2012.02.003
DO - 10.1016/j.anihpc.2012.02.003
M3 - Article
AN - SCOPUS:84864130981
SN - 0294-1449
VL - 29
SP - 637
EP - 652
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -