Access the full text.
Sign up today, get DeepDyve free for 14 days.
(1980)
Decay of parabolic conservation laws
P Han (2016)
Large time behavior for the nonstationary Navier-Stokes flows in the half-spaceAdv. Math., 288
P. Han (2014)
Weighted spatial decay rates for the Navier–Stokes flows in a half-spaceProceedings of the Royal Society of Edinburgh: Section A Mathematics, 144
Jiahong Wu (2001)
Dissipative quasi-geostrophic equations with L p data
H Bae, B Jin (2012)
Existence of strong mild solution of the Navier-Stokes equations in the half space with nondecaying initial dataJ. Korean Math. Soc., 49
V. Solonnikov (2003)
On Nonstationary Stokes Problem and Navier–Stokes Problem in a Half-Space with Initial Data Nondecreasing at InfinityJournal of Mathematical Sciences, 114
Jiahong Wu (2005)
Global Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov SpacesSIAM J. Math. Anal., 36
P Han (2014)
10.1016/j.jfa.2013.11.025J. Funct. Anal., 266
ME Schonbek (1992)
10.1512/iumj.1992.41.41042Indiana Univ. Math. J., 41
Hyeong‐Ohk Bae (2008)
Temporal and Spatial Decays for the Stokes FlowJournal of Mathematical Fluid Mechanics, 10
M. Schonbek (1985)
L2 decay for weak solutions of the Navier-Stokes equationsArchive for Rational Mechanics and Analysis, 88
W. Borchers, T. Miyakawa (1988)
L2 decay for the Navier-Stokes flow in halfspacesMathematische Annalen, 282
Jiahong Wu (2002)
THE QUASI-GEOSTROPHIC EQUATION AND ITS TWO REGULARIZATIONSCommunications in Partial Differential Equations, 27
Jiahong Wu (2005)
The two-dimensional quasi-geostrophic equation with critical or supercritical dissipationNonlinearity, 18
(1987)
Integrals and derivatives of fractional order and some their applications
W Borchers, T Miyakawa (1988)
$$L^2$$ L 2 decay for the Navier-Stokes flow in half spacesMath. Ann., 282
Hyeong‐Ohk Bae, B. Jin (2012)
EXISTENCE OF STRONG MILD SOLUTION OF THE NAVIER-STOKES EQUATIONS IN THE HALF SPACE WITH NONDECAYING INITIAL DATAJournal of Korean Medical Science, 49
ME Schonbek (1995)
Large time behaviour of solutions to the Navier-Stokes equations in $$H^m$$ H m spacesCommun. Partial Differ. Equ., 20
Hyeong‐Ohk Bae, B. Jin (2005)
Upper and lower bounds of temporal and spatial decays for the Navier–Stokes equationsJournal of Differential Equations, 209
ME Schonbek (1995)
10.1080/03605309508821088Commun. Partial Differ. Equ., 20
L. Brandolese, 1. FrancoisVigneronUniversit'edeLyon, E. Cmls (2007)
New asymptotic profiles of nonstationary solutions of the Navier–Stokes systemJournal de Mathématiques Pures et Appliquées, 88
Vladimir Clue (2004)
Harmonic analysis2004 IEEE Electro/Information Technology Conference
H Bae (2006)
Temporal decays in $$L^1$$ L 1 and $$L^\infty $$ L ∞ for the Stokes flowJ. Differ. Equ., 222
(2014)
Long - time behavior for the nonstationary Navier – Stokes flows in L 1 ( R n + )
Hyeong‐Ohk Bae (2005)
Temporal and spatial decays for the Navier–Stokes equationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 135
J. Leray (1934)
Sur le mouvement d'un liquide visqueux emplissant l'espaceActa Mathematica, 63
(1995)
The Fourier Splitting Method
S. Ukai (1987)
A solution formula for the Stokes equation in RnCommunications on Pure and Applied Mathematics, 40
P. Constantin, Jiahong Wu (1999)
Behavior of solutions of 2D quasi-geostrophic equationsSiam Journal on Mathematical Analysis, 30
P. Han (2012)
Weighted decay properties for the incompressible Stokes flow and Navier–Stokes equations in a half spaceJournal of Differential Equations, 253
M. Schonbek (1992)
Asymptotic behavior of solutions to the three-dimensional Navier-Stokes equationsIndiana University Mathematics Journal, 41
ME Schonbek (1980)
10.1080/0360530800882145Commun. Partial Differ. Equ., 7
M. Schonbek, M. Wiegner (1996)
On the decay of higher-order norms of the solutions of Navier–Stokes equationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 126
Yoshiko Fujigaki, T. Miyakawa (2001)
Asymptotic profiles of nonstationary incompressible Navier–Stokes flows in the half-spaceMethods and applications of analysis, 8
Jiahong Wu (2002)
The 2D dissipative quasi-geostrophic equationAppl. Math. Lett., 15
ME Schonbek (1985)
$$L^2$$ L 2 decay for weak solutions of the Navier-Stokes equationsArch. Rational Mech. Anal., 88
H Bae (2006)
10.1016/j.jde.2005.01.001J. Differ. Equ., 222
Jiahong Wu (2005)
Solutions of the 2D quasi-geostrophic equation in Hölder spacesNonlinear Analysis-theory Methods & Applications, 62
M. Schonbek (1991)
Lower bounds of rates of decay for solutions to the Navier-Stokes equationsJournal of the American Mathematical Society, 4
P Han (2016)
10.1016/j.aim.2015.10.010Adv. Math., 288
L. Brandolese (2003)
Space-time decay of Navier–Stokes flows invariant under rotationsMathematische Annalen, 329
J Wu (2005)
Solutions of the 2D quasi-geostrophic equation in $$\text{H}\ddot{o}\text{lder}$$ H o ¨ lder spacesNonlinear Anal., 62
There is a long standing problem on the nonstationary Navier–Stokes equations which pertains to how to characterize the L 1−time asymptotic expansion of the Navier–Stokes flows in the half space. Beyond a few partial results, new progress has not yet to be made on this open question. In this article, we give a confirmed answer to this problem; namely, a thorough characterization on L 1−summability is revealed. In order to prove this result, we need to avoid the unboundedness of the projection operator, which is overcome by treating an elliptic Neumann problem. Finally, using the weighted estimates on the heat kernel’s convolution, we obtain the exact profile structure of the asymptotic expansion in $${L^1(\mathbb{R}^n_+)}$$ L 1 ( R + n ) . In addition, some crucial estimates on the fractional spatial derivatives of the non-stationary Stokes and Navier–Stokes flows are established for the first time, which allows for a better understanding of the L 1−decay problem.
Archive for Rational Mechanics and Analysis – Springer Journals
Published: Jun 1, 2018
Access the full text.
Sign up today, get DeepDyve free for 14 days.