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P. Lemarié–Rieusset (2002)
Recent Developments in the Navier-Stokes Problem
Simão Correia, M'ario Figueira (2016)
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Tosio Kato (1984)
StrongLp-solutions of the Navier-Stokes equation inRm, with applications to weak solutionsMathematische Zeitschrift, 187
Lisboa Portugal e-mail: sfcorreia@fc.ul.pt Mário Figueira e-mail: msfigueira@fc.ul.pt (accepted: February 8
J. Ginibre, G. Velo (1996)
The Cauchy problem in local spaces for the complex Ginzburg-Landau equation I: compactness methodsPhysica D: Nonlinear Phenomena, 95
(1962)
On the non-stationary Navier–Stokes system
T Kato (1984)
Strong $$L^p$$ L p -solutions of the Navier–Stokes equation in $${\mathbb{R}}^m$$ R m , with applications to weak solutionsMath. Z., 187
J. Ginibre, G. Velo (1997)
The Cauchy Problem in Local Spaces for the Complex Ginzburg—Landau Equation¶II. Contraction MethodsCommunications in Mathematical Physics, 187
(2001)
On self-similar solutions of the complex Ginzburg–Landau equation
We consider the three-dimensional incompressible Navier–Stokes equation on the whole space. We observe that this system admits a $$L^\infty $$ L ∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes $$L^3(\mathbb {R}^3)$$ L 3 ( R 3 ) and these solutions. Finally, we prove $$L^3$$ L 3 -stability of spatial plane waves, with no condition on their size.
Journal of Mathematical Fluid Mechanics – Springer Journals
Published: Feb 21, 2017
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