On the global regularity of N -dimensional generalized Boussinesq system

Kazuo Yamazaki

Applications of Mathematics (2015)

  • Volume: 60, Issue: 2, page 109-133
  • ISSN: 0862-7940

Abstract

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We study the N -dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.

How to cite

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Yamazaki, Kazuo. "On the global regularity of $N$-dimensional generalized Boussinesq system." Applications of Mathematics 60.2 (2015): 109-133. <http://eudml.org/doc/269885>.

@article{Yamazaki2015,
abstract = {We study the $N$-dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.},
author = {Yamazaki, Kazuo},
journal = {Applications of Mathematics},
keywords = {Boussinesq system; global regularity; regularity criteria; Besov space; Boussinesq system; global regularity; regularity criteria; Besov space},
language = {eng},
number = {2},
pages = {109-133},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the global regularity of $N$-dimensional generalized Boussinesq system},
url = {http://eudml.org/doc/269885},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Yamazaki, Kazuo
TI - On the global regularity of $N$-dimensional generalized Boussinesq system
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 109
EP - 133
AB - We study the $N$-dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.
LA - eng
KW - Boussinesq system; global regularity; regularity criteria; Besov space; Boussinesq system; global regularity; regularity criteria; Besov space
UR - http://eudml.org/doc/269885
ER -

References

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