The drift-diffusion system in two-dimensional critical Hardy space

Takayoshi Ogawa, Senjo Shimizu

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1107-1138
Number of pages32
JournalJournal of Functional Analysis
Issue number5
Publication statusPublished - 2008 Sept 1


  • Drift-diffusion system
  • Hardy space
  • Large data local existence
  • Small data global existence


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