Well-posedness for the Navier–Stokes Equations

By Herbert Koch, D. Tataru. 2001

1,051 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c5ac8d19f88f2abb7aed72ab12cae305bdd89992

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

An alternative approach to regularity for the Navier–Stokes equations in critical spaces (2009, methodology): “In order to do this, we turn to the local solutions u(KT ) of Koch-Tataru [34] for (possibly large, but somewhat regular) initial data in the space bmo−1, and a “persistency” theorem given in [18] which states that whenever the initial datum belongs to various spaces of regular data, including Ḣ 1 ”
Forward Discretely Self-Similar Solutions of the Navier–Stokes Equations (2014, background): “These solutions would necessarily involve large data but, until recently, existence results for self-similar solutions were only known for small data (for small data existence of forward self-similar solutions see [1,4,7,12,14]).”
Non-uniqueness of Leray solutions of the forced Navier-Stokes equations (2021, background): “For |σ| ≪ 1, existence and uniqueness falls into the known perturbation theory of Koch and Tataru [35] in BMO, for example.”
Multipliers, paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations (2006, background): “In the following theorem, the existence part is due to Koch and Tataru [22], and the uniqueness to Miura [35].”
Navier–Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices (2010, background): “In the following Theorem 1.3 for Navier–Stokes equations, our initial data is included in the results by Koch and Tataru [14] in some cases, and the other cases are not clear in general.”
Wellposedness and stability results for the Navier-Stokes equations in ${\mathbf R}^{3}$ (2006, methodology): “ while P(x,R) = [0,R2]×B(x,R) and B(x,R) denotes the ball of R3 of center xand radius R. Let us point out that, in the case when λ= 0, this is exactly the space introduced by H. Koch and D. Tataru in [15], and that for any λ≥ 0 we have due to (2.1), (2.3) kvkλ ≤ kvk0 ≤ Ckvkλ exp Cλku0k4 B˙−1 ∞,2 .”
Global solutions for the Navier-Stokes equations in the rotational framework (2013, methodology): “On the well-posedness for (NSC) with ⌦ = 0 in the scaling invarint spaces, we refer to FujitaKato [7], Kato [14], Kozono-Yamazaki [19], Koch-Tataru [17].”
Geometric flows with rough initial data (2009, methodology): “Similar function spaces have been used in [12] to construct a solution to the NavierStokes equation.”
Convex integration and phenomenologies in turbulence (2019, background): “1, if one considers the family of Banach spaces CtH x , then α∗ = αWP = 1/2 [84, 109, 113, 127, 11].”
The Navier-Stokes equations and weak Herz spaces (2011, background): “3 where p > n and q < ∞, then the initial data was dealt in [24].”
A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations (2010, neutral): “See the interesting work by Koch and Tataru [16].”