Bilinear estimates in BMO and the Navier-Stokes equations

By H. Kozono, Y. Taniuchi. 2000

312 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/54246b60e334bbc0bfd7487ef76eefa9508d3b52

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In Applied Mathematics

1. Dongho Chae
2. Zhifei Zhang
3. Changxing Miao
4. Sadek Gala
5. Jiahong Wu
6. Qionglei Chen
7. Zhen Lei
8. Baoquan Yuan

In Mathematical Physics

1. Dongho Chae
2. Zhifei Zhang
3. Sadek Gala
4. Changxing Miao
5. Jiahong Wu
6. Zhen Lei
7. Qionglei Chen
8. Alexis Vasseur

Citations in the corpus

• Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations (2005, background): “Taniuchi in [123] considered the marginal case s = 2, r = ∞ in a larger class, say v2 ∈ L(2)((0, T ); BMO)).”
• Interior regularity criteria in weak spaces for the Navier-Stokes equations (2004, background): “Theorem 2 covers the whole range of values of r except one critical value r =∞ . On the other hand, a global version (in space) of Theorem 2 was obtained by Sohr [15] for the non-critical case 3 9 ] for r =∞ and very recently by Iskauriaza, Ser¨ egin and Shverak [3] for r = 3. Hence ...”
• 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.”
• On the Regularity Conditions for the Navier-Stokes and Related Equations (2005, unknown): “After that there are further developments and refinements by Serrin ([29]), Fabes-Jones-Riviere ([20]), KozonoTaniuchi ([22]), and Escauriaza-Sverak-Seregin ([19]).”
• Remark on uniqueness of weak solutions to the Navier–Stokes equations (2008, result): “The replacement of hypothesis u ∈ L2((0, T ); L∞) by u ∈ L2((0, T ); BMO(Rd)d) was recently discussed in a similar context by Kozono and Taniuchi [8].”
• The Navier-Stokes equations and weak Herz spaces (2011, background): “Such a problem was considered by Beale, Kato and Majda [3], Giga [12], Kozono and Taniuchi [29], Kozono, Ogawa and Taniuchi [27] and Kozono and Shimada [28].”
• Multipliers, paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations (2006, methodology): “The other limit case, namely P = L 2 ([0, T ], BM O) was treated by Kozono and Taniuchi [23].”
• Regularity criterion for 3d navier-stokes equations in terms of the direction of the velocity (2007, background): “This condition was later improved to L(1)(BMO) by Kozono and Taniuchi [9].”
• On Kato–Ponce and fractional Leibniz (2016, methodology): “[16] Kozono, Hideo and Taniuchi, Yasushi.”
• BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity (2009, background): “2) At last, let us recall the following logarithmic Sobolev inequality which is proved in [15] and is an improved version of that in [1] (see also [2, 3]).”
• On the Interior Regularity of Suitable Weak Solutions to the Navier–Stokes Equations (2007, methodology): “We also reference Kozono and Taniuchi (2000) for a refinement of the case p = , q = 2, replacing v L2 t x by( ∫ T 0 v 2BMOdt ) 1 2 .”
• Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in R 3 (2005, background): “In the marginal caser = ∞, Kozono and Taniuchi[15] proved the regularity of weak solutions under the condition curlu ∈ L1(0, T ;BMO), (1.4) where BMO is the space of the bounded mean oscillation defined by f ∈ L1loc(R3), sup x,R 1 |BR| ∫ BR(x) |f (y)− f̄BR(x)| dy <∞, where f̄BR(x) is the average of ”
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations (2002, background): “The critical Sobolev inequalities in Besov spaces 263 Proposition 3.3 (Kozono-Taniuchi [ 26 ]).”
• A New Regularity Criterion for the Navier-Stokes Equations in Terms of the Gradient of One Velocity Component (2002, background): “Recently Kozono and Taniuchi [ 9 ] showed that if a Leray-Hopf weak solution u(x,t) ∈ L2(0,T;BMO), then u(x,t)is actually a strong solution of (1) on (0,T).”
• Log Improvement of the Prodi-Serrin Criteria for Navier-Stokes Equations (2007, background): “Beale Kato and Majda [1] showed the global regularity under the condition that the vorticity ω = curl u lies in L∞(0,∞;L1(R3)) (see Kozono and Taniuchi for improvement of this result [13]).”
• Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain (2004, background): “Recently Kozono and Taniuchi [15] showed that if a Leray-Hopf weak solution u(x, t) ∈ L2(0, T ;BMO), then u(x, t)is actually a strong solution of (1) on (0, T ).”
• Limiting Case of the Sobolev Inequality in BMO,¶with Application to the Euler Equations (2000, methodology): “Moreover, we can formulate the continuation principle for u itself in L 2 (0 ,T ; BMO). For details, see [ 9 ].”