An Extension of the Beale-Kato-Majda Criterion for the Euler Equations

61 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Global well posedness for the Maxwell-Navier-Stokes system in 2D (2010, methodology): “Also, (35) is used by Beale, Kato and Majda [3] to give a non-blow up criterion of 3D incompressible Euler (see also [18,29]).”
Remarks on the blowup criteria for Oldroyd models (2009, result): “Hence, we have the following corollary where we also use the improved criterion of Planchon.”
A review of the mean field limits for Vlasov equations (2014, background): “Uniqueness usually requires ρ ∈ L∞, [103], [160] (see [138] for an extension to the critical Besov space).”
The Beale-Kato-Majda Criterion for the 3D Magneto-Hydrodynamics Equations (2007, methodology): “8), it can be referred to the remarks after Theorem 1 in [15].”
Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients (2005, methodology): “Planchon to improve the Beale-Kato-Majda blow-up criterion ([17]).”
Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations (2005, background): “The idea is that if some additional integrability property is satisfied by at least one weak solution, more exactly, if v2 ∈ L((0, T );Lr) and if 2/s + n/r = 1 with n < r ∞, then all weak solutions have to coincide with it (recently, Kozono and Taniuchi in [126] considered the marginal case s = 2, r”