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Uspekhi Mat. Nauk, 2004, Volume 59, Issue 6(360), Pages 55–72 (Mi umn795)  

This article is cited in 7 scientific papers (total in 7 papers)

On solutions with infinite energy and enstrophy of the Navier–Stokes system

Yu. Yu. Bakhtina, E. I. Dinaburga, Ya. G. Sinaibc

a International Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Princeton University, Department of Mathematics

Abstract: The Cauchy problem is considered for the Navier–Stokes system. Local and global existence and uniqueness theorems are given for initial data whose Fourier transform decays at infinity as a power-law function with negative exponent and has a power-law singularity at zero. The paper contains a survey of known facts and some new results.

DOI: https://doi.org/10.4213/rm795

Full text: PDF file (326 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2004, 59:6, 1061–1078

Bibliographic databases:

UDC: 517.957
MSC: Primary 35Q30; Secondary 35A05, 35A07, 76D05
Received: 14.10.2004

Citation: Yu. Yu. Bakhtin, E. I. Dinaburg, Ya. G. Sinai, “On solutions with infinite energy and enstrophy of the Navier–Stokes system”, Uspekhi Mat. Nauk, 59:6(360) (2004), 55–72; Russian Math. Surveys, 59:6 (2004), 1061–1078

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sinai Ya., “Power series for solutions of the 3D-Navier–Stokes system on $R^3$”, J. Stat. Phys., 121:5-6 (2005), 779–803  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. M. D. Arnold, “Local existence theorem for the solutions of the $d$-dimensional system of Navier–Stokes equations”, Russian Math. Surveys, 60:3 (2005), 562–563  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Sinai Ya., “Absence of the local existence theorem in the critical space for the 3D-Navier–Stokes system”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 15:11 (2005), 3635–3637  crossref  mathscinet  zmath  isi  elib
    4. Bakhtin Yu., “Existence and uniqueness of stationary solutions for 3D Navier–Stokes system with small random forcing via stochastic cascades”, J. Stat. Phys., 122:2 (2006), 351–360  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Sinai Ya., “A new approach to the study of the 3D-Navier–Stokes system”, Prospects in Mathematical Physics, Contemporary Mathematics Series, 437, 2007, 223–229  crossref  mathscinet  zmath  isi
    6. Albeverio S., Ferrario B., “Some methods of infinite dimensional analysis in hydrodynamics: An introduction”, SPDE in hydrodynamic: recent progress and prospects, Lecture Notes in Math., 1942, Springer, Berlin, 2008, 1–50  crossref  mathscinet  zmath  isi  elib
    7. Orum Ch., Ossiander M., “Exponent Bounds for a Convolution Inequality in Euclidean Space with Applications to the Navier–Stokes Equations”, Proc. Amer. Math. Soc., 141:11 (2013), 3883–3897  crossref  mathscinet  zmath  isi  elib
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