\(L^p\)-bounds for quasi-geostrophic equations via functional analysis. (English) Zbl 1272.35165
J. Math. Phys. 52, No. 8, 083101, 12 p. (2011); erratum 54, No. 7, 079902, 1 p. (2013).
Summary: We give a proof of \(L^p\)-bounds for the quasi-geostrophic equation and other non-local equations. The proof uses mainly tools from functional analysis, notably the product formulas (also known as “operator splitting methods”) and the Bochner-Pollard subordination identities, hence it could be applicable to other equations. {
©2011 American Institute of Physics}
Editorial remark: In the erratum, an incorrect numbering of the references is fixed: References 1-13 should be the next one, Ref 14 should be Ref 16, Ref 15 should be Ref 1, Ref 16 should be Ref 15.
©2011 American Institute of Physics}
Editorial remark: In the erratum, an incorrect numbering of the references is fixed: References 1-13 should be the next one, Ref 14 should be Ref 16, Ref 15 should be Ref 1, Ref 16 should be Ref 15.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76E20 | Stability and instability of geophysical and astrophysical flows |
| 76U05 | General theory of rotating fluids |
| 86A05 | Hydrology, hydrography, oceanography |
| 86A10 | Meteorology and atmospheric physics |
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