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Russian Mathematical Surveys, 2014, Volume 69, Issue 3, Pages 395–418
DOI: https://doi.org/10.1070/RM2014v069n03ABEH004896 (Mi rm9590) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Local formulae for the hydrodynamic pressure and applications

P. Constantin

Princeton University, Princeton, USA
English version PDF (528 kB) Citations (9)
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DOI: https://doi.org/10.1070/RM2014v069n03ABEH004896
Abstract: We provide local formulae for the pressure of incompressible fluids. The pressure can be expressed in terms of its average and averages of squares of velocity increments in arbitrarily small neighbourhoods. As an application, we give a brief proof of the fact that $C^{\alpha}$ velocities have $C^{2\alpha}$ (or Lipschitz) pressures. We also give some regularity criteria for 3D incompressible Navier–Stokes equations.
Bibliography: 9 titles.
Keywords: Navier–Stokes equations, Euler's equations, pressure, regularity criteria.
Funding agency Grant number
National Science Foundation NSF-DMS 1209394
NSF-DMS 1265132
This research was partially supported by the grants NSF-DMS 1209394 and NSF-DMS 1265132.
Received: 27.10.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2014, Volume 69, Issue 3(417), Pages 3–26
DOI: https://doi.org/10.4213/rm9590
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35Q35
Language: English
Original paper language: Russian
Citation: P. Constantin, “Local formulae for the hydrodynamic pressure and applications”, Uspekhi Mat. Nauk, 69:3(417) (2014), 3–26; Russian Math. Surveys, 69:3 (2014), 395–418
Citation in format AMSBIB
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\transl
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  • https://www.mathnet.ru/eng/rm/v69/i3/p3
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:626
    Russian version PDF:190
    English version PDF:16
    References:61
    First page:29
     
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