Semantic Scholar Open Access 2007 118 sitasi

Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations

P. Constantin Jiahong Wu

Lihat Sumber DOI

Abstrak

Abstract We examine the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical ( α 1 / 2 ) dissipation ( − Δ ) α . This study is motivated by a recent work of Caffarelli and Vasseur, in which they study the global regularity issue for the critical ( α = 1 / 2 ) QG equation [L. Caffarelli, A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, arXiv: math.AP/0608447, 2006]. Their approach successively increases the regularity levels of Leray–Hopf weak solutions: from L 2 to L ∞ , from L ∞ to Holder ( C δ , δ > 0 ), and from Holder to classical solutions. In the supercritical case, Leray–Hopf weak solutions can still be shown to be L ∞ , but it does not appear that their approach can be easily extended to establish the Holder continuity of L ∞ solutions. In order for their approach to work, we require the velocity to be in the Holder space C 1 − 2 α . Higher regularity starting from C δ with δ > 1 − 2 α can be established through Besov space techniques and will be presented elsewhere [P. Constantin, J. Wu, Regularity of Holder continuous solutions of the supercritical quasi-geostrophic equation, Ann. Inst. H. Poincare Anal. Non Lineaire, in press].

Topik & Kata Kunci

Mathematics

Penulis (2)

P. Constantin

Jiahong Wu

Format Sitasi

APA MLA BibTeX

Constantin, P., Wu, J. (2007). Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations. https://doi.org/10.1016/J.ANIHPC.2007.10.002

Akses Cepat

Lihat di Sumber doi.org/10.1016/J.ANIHPC.2007.10.002

Informasi Jurnal

Tahun Terbit: 2007
Bahasa: en
Total Sitasi: 118×
Sumber Database: Semantic Scholar
DOI: 10.1016/J.ANIHPC.2007.10.002
Akses: Open Access ✓