MR2239910
Taniuchi, Yasushi
Yasushi TANIUCHI
Remarks on Global Solvability of 2-D Boussinesq Equations with Non-Decaying Initial Data
Funkcialaj Ekvacioj. Serio Internacia
49
2006
39--57
http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-1/49_39.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2239910
We show the global existence theorem for the two-dimensional Boussinesq equations in the entire plane with non-decaying initial data. To this end, we give an estimate of the vorticity in the uniformly local Lebesgue space.
2-D Boussinesq equations, Non-Decaying initial data, Global solution.
35Q35.
49-39
2006
Remarks on Global Solvability of 2-D Boussinesq Equations with Non-Decaying Initial Data
TANIUCHI, Yasushi
Yasushi TANIUCHI
1
Beale, J. T.; Kato, T.; Majda, A.
Remarks on the breakdown of smooth solutions for the 3-D Euler equations
Comm. Math. Phys.
94
1984
61-66
MR0763762
2
Bergh, J.; Löfström, J.
Interpolation spaces, An introduction
Berlin-New York-Heidelberg, Springer-Verlag
1976
MR0482275
3
Cannon, J. R.; DiBenedetto, E.
The initial value problem for Boussinesq equations with data in $L^p$, Approximation Methods for Navier-Stokes problems
Edited by Rautmann, R., Lect. Notes in Math.
771
1980
129-144
MR0565993
4
Cannon, J. R.; Knightly, G. H.
A note on the Cauchy problem for the Navier-Stokes equations
SIAM J. Appl. Math.
18
1970
641-644
MR0270004
5
Cannone, M.
Ondelettes, Paraproduits et Navier-Stokes
Diderot Editeur, Arts et Sciences Paris-New York-Amsterdam
1995
MR1688096
6
Foias, C.; Manley, O.; Temam, R.
Attractors for the Bénard problem: existence and physical bounds of their fractal dimension
Nonlinear Anal. T. M. A.
11
1987
939-967
MR0903787
7
Fife, P. C.; Joseph, D. D.
Existence convictive solutions of the generalized Benard problem which are analytic in their norm.
Arch. Rational Mech. Anal.
33
1969
116-138
MR0239811
8
Hishida, T.
Existence and Regularizing properties of solutions for the nonstationary convection problem
Funkcial. Ekvac.
34
1991
449-474
MR1150874
1150874
9
Hishida, T.; Yamada, Y.
Global solutions for the heat convection equations in an exterior domain
Tokyo J. Math.
15
1992
135-151
MR1164192
10
Giga, Y.; Giga, M.-H.
Nonlinear Partial Differential equations
Kyoritsu Shuppan (in Japanese)
1999
11
Giga, Y.; Inui, K.; Matsui, S.
On the Cauchy problem for the Navier-Stokes equations with nondecaying initial data
Quad. Mat.
4
1999
27-68
MR1770188
12
Giga, Y.; Inui, K.; Kato, J.; Matsui, S.
Remarks on uniqueness of bounded solutions of the Navier-Stokes equations
Nonlinear Anal.
47
2001
4151-4156
MR1972355
13
Giga, Y.; Matsui, S.; Sawada, O.
Global Existence of Two-Dimensional Navier-Stokes Flow with Nondecaying Initial Velocity
J. Math. Fluid Mech.
3
2001
302-315
MR1860126
14
Ishimura, N.; Morimoto, H.
Remarks on the blow-up criterion for the 3-D Boussinesq equations
Math. Models Methods Appl. Sci.
9
1999
1323-1332
MR1725820
15
Kagei, Y.
On weak solutions of nonstationary Boussinesq equations
Differential Integral Equations
6
1993
587-611
MR1202559
16
Kagei, Y.; von Wahl, W.
The Eckhaus criterion for convection roll solutions of the Oberbeck-Boussinesq equations
Internat. J. Non-Linear Mech.
32
1997
563-620
MR1434157
17
Kato, J.
The uniqueness of nondecaying solutions of the Navier-Stokes equations
Arch. Rational Mech. Anal.
169
2003
159-175
MR2005640
18
Koch, H.; Tataru, D.
Well-posedness for the Navier-Stokes equations
Adv. Math.
157
2001
22-35
MR1808843
19
Kozono, H.; Ogawa, T.; Taniuchi, Y.
Navier-Stokes equations in the Besov space near $L^\infty$ and BMO
Kyushu J. Math.
57
2003
303-324
MR2050088
20
Kozono, H.; Yamazaki, M.
Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data
Comm. Partial Differential Equations
19
1994
959-1014
MR1274547
21
Morimoto, H.
On the existence of weak solutions of equation of natural convection
J. Fac. Sci. Univ. Tokyo, Sect. IA Math.
36
1989
87-102
MR0991021
22
Morimoto, H.
Non-stationary Boussinesq equations
J. Fac. Sci. Univ. Tokyo, Sect. IA Math.
39
1992
61-75
MR1157977
23
Oeda, K.
On the initial Value problem for the heat convection equation of Boussinesq approximation in a time-depended domain.
Proc. Japan Acad., Ser A Math. Sci.
64
1988
143-146
MR0965951
24
Oeda, K.
Weak and strong solutions of the heat convection equations in regions with moving boundaries
J. Fac. Sci. Univ. Tokyo, Sect. IA Math.
36
1989
491-536
MR1039484
25
Sawada, O.
On time-local solvability of the Navier-Stokes equations in Besov spaces
Adv. Differential Equations
8
2003
385-412
MR1972594
26
Sawada, O.; Taniuchi, Y.
On Boussinesq flow with nondecaying initial data
Funkcial. Ekvac.
47
2004
225-250
MR2108674
2108674
27
Serfati, P.
Solutions $C^\infty$ en temps, $n$-log lipchitz bornées en espace et équation d'Euler
C. R. Acad. Sci. Paris Sér. I Math.
320
1995
555-558
MR1322336
28
Taniuchi, Y.
Uniformly local $L^p$ estimate for 2-D vorticity equation and its application to Euler equations with initial vorticity in bmo
Comm. Math. Phys.
248
2004
169-186
MR2104609
29
Triebel, H.
Theory of Function Spaces
Birkhäuser, Basel-Boston-Stuttgart
1983
MR0781540
30
Triebel, H.
Theory of Function Spaces II
Birkhäuser, Basel-Boston-Stuttgart
1992
MR1163193
31
Vishik, M.
Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
Ann. Sci. École Norm. Sup.
32
1999
769-812
MR1717576