The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

By H. Kozono, T. Ogawa, Y. Taniuchi. 2002

356 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/32545cab4683e4baafd8c028d886de55f0b1992b

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In Applied Mathematics

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Citations in the corpus

On the Regularity Criterion of Weak Solution for the 3D Viscous Magneto-Hydrodynamics Equations (2007, methodology): “In the case of s = 0 or s = 1, Kozono, Ogawa and Taniuchi[14] proved the similar results for the Navier-Stokes equations by using the Logarithmic Sobolev inequality in the Besov spaces.”
Global strong solution to the 2D nonhomogeneous incompressible MHD system (2012, background): “The proof follows exactly that in [23] and lies mainly on the Littlewood-Paley decomposition.”
Bilinear estimates in homogeneous Triebel‐Lizorkin spaces and the Navier‐Stokes equations (2004, methodology): “In this direction, Kozono–Ogawa–Taniuchi [14] proved that if the smooth solution u satisfies either u ∈ L2(0, T ; Ḟ 0∞,∞) or rot u ∈ L1(0, T ; Ḟ 0∞,∞) , (0.2) then u(t) can be continued as the smooth solution beyond T .”
Remarks on Gagliardo–Nirenberg type inequality with critical Sobolev space and BMO (2008, background): “6) in terms of the L p − Lq estimate for the semigroup {e−t (− )s/2}t 0, which is different from [9] and Engler [7].”
The Beale-Kato-Majda Criterion for the 3D Magneto-Hydrodynamics Equations (2007, background): “For the Navier-Stokes equations (with b = 0 in (1.1)), Kozono, Taniuchi [10], and Kozono, Ogawa, Taniuchi [11] refined the Beale-Kato-Majda criterion to ∫ T 0 ‖∇ × u(t)‖BMOdt ∞ and ∫ T 0 ‖∇ × u(t)‖Ḃ0 ∞,∞ dt ∞, respectively.”
On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space (2010, background): “Later, many improvements and extensions were established; for example, see [15, 13, 14, 32] and the references therein.”
Local Well-Posedness and Blowup Criterion of the Boussinesq Equations in Critical Besov Spaces (2010, background): “Since there on, different authors improved the similar result, see [10, 11, 12, 15, 8, 16] and so on.”
Regularity Criteria for the Generalized MHD Equations (2008, background): “( 2002 ) to where <inline-graphic xmlns:xlink="http://www.”
Extension criterion via two-components of vorticity on strong solutions to the 3 D Navier-Stokes equations (2004, background): “Kozono-Ogawa-Taniuchi [ 17 ] generalized the results of [1] and [16] to the space L 1 (0 ,T ; ˙ ∞,∞), where ˙ B 0 ∞,∞ denotes the homogeneous Besov space.”
On the well-posedness of the incompressible density-dependent Euler equations in the Lp framework (2009, methodology): “Hence, repeating the proof of Lemma 5 and using the logarithmic interpolation inequality of [15] yields the result.”