The second iterate for the Navier–Stokes equation

By Pierre Germain. 2008

84 citations recorded by the source corpus.

We consider the iterative resolution scheme for the Navier–Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch–Tataru solutions; a first step towards weak–strong uniqueness for Koch–Tataru solutions; and finally an instability result in B˙∞,q−1, for q>2.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7e11bfc6ea3df1911b6ec1e7513c1e8de1863ed4

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Ill-posedness of the 3D-Navier–Stokes equations in a generalized Besov space near BMO−1 (2010, background): “The idea of setting of the initial data is proposed by [2] and [4].”
Global regularity for some classes of large solutions to the Navier-Stokes equations (2008, background): “thus seems that the Koch-Tataru theorem is optimal for the wellposedness of the Navier-Stokes equations — note that it was very recently proved (see [14] and [1]) that the equations are in fact ill-posed in Ḃ−1 ∞,∞.”
ON THE ILL-POSEDNESS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS (2011, methodology): “Our proof is inspired by Germain’s paper [13], where the author proved the ill-posedness of the incompressible Navier-Stokes equations in Besov space Ḃ−1 ∞,∞(see also a different proof by Bourgain-Pavlović [1]).”
Ill-posedness of the Navier-Stokes equations in a critical space in 3D (2008, methodology): “[7] P. Germain, The second iterate for the Navier-Stokes equation, Preprint (2008), arXiv:0806.4525.”