TY - JOUR
T1 - The drift-diffusion system in two-dimensional critical Hardy space
AU - Ogawa, Takayoshi
AU - Shimizu, Senjo
N1 - Funding Information:
Work of T. Ogawa is partially supported by JSPS Grant-in-aid for Scientific Research B #15340056 and A #20244009. Work of S. Shimizu is partially supported by JSPS Grant-in-aid for Scientific Research C #20540164.
PY - 2008/9/1
Y1 - 2008/9/1
N2 - We establish the time local well-posedness for large data of a solution to two-dimensional drift-diffusion system in the critical Hardy space H1 (R2). This solution is obtained in the Hardy class, for which the natural free energy is well defined from the initial time. The time global well-posedness result for small data is also obtained in a similar class. The crucial parts of the proof are to employ the end-point type of maximal regularity for the homogeneous heat equation and some new bilinear estimates in the Hardy space.
AB - We establish the time local well-posedness for large data of a solution to two-dimensional drift-diffusion system in the critical Hardy space H1 (R2). This solution is obtained in the Hardy class, for which the natural free energy is well defined from the initial time. The time global well-posedness result for small data is also obtained in a similar class. The crucial parts of the proof are to employ the end-point type of maximal regularity for the homogeneous heat equation and some new bilinear estimates in the Hardy space.
KW - Drift-diffusion system
KW - Hardy space
KW - Large data local existence
KW - Small data global existence
UR - http://www.scopus.com/inward/record.url?scp=48949115041&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=48949115041&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2008.05.020
DO - 10.1016/j.jfa.2008.05.020
M3 - Article
AN - SCOPUS:48949115041
SN - 0022-1236
VL - 255
SP - 1107
EP - 1138
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 5
ER -