Localization in Fourier space and Navier-Stokes system

By Jean-Yves Chemin. 2005

138 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5092dc3163221f98f9d031b8ef65be1c86d4e5c6

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1. Jiang Xu
2. Changxing Miao
3. R. Thompson
4. Shuichi Kawashima
5. Qionglei Chen
6. John Holmes
7. Yemin Chen
8. Zhen Lei

Citations in the corpus

• On the Cauchy problem for the two-component Camassa–Holm system (2011, methodology): “1 [7] (Bernstein’s inequality) Let B be a ball with center 0 in Rd and C a ring with center 0 in Rd .”
• Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces (2016, methodology): “In this section, we will recall some conclusions on the properties of Littlewood-Paley decomposition, the Besov spaces and the theory of the transport equation which can be seen in [5], [7, 8, 9], [30].”
• On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, background): “Littlewood–Paley analysis For convenience of the reader, we shall recall some basic facts on the Littlewood–Paley theory, one may check [1,6,7,16,32] for more details.”
• The Global Existence of Small Solutions to the Incompressible Viscoelastic Fluid System in 2 and 3 Space Dimensions (2006, methodology): “To overcome the additional difficulty caused by the whole space domain here instead of bounded domain case in Kawashima and Shibata (1992), we introduce a quantity M def = v− F which will play the same roles as w in Lin et al.”
• Global well-posedness for the micropolar fluid system in critical Besov spaces (2010, methodology): “We will adopt the spirit of the proof for heat operators as in [7].”
• Global Well-Posedness for Compressible Viscoelastic Fluids near Equilibrium (2010, unknown): “Let {ek(t)}k∈Z be a sequence defined in [0,+∞) satisfying the following conditions: ek(t) ∈ [0, 1], ek(t) ek′(t) if k k′, C−1ek′(t) ek(t) Cek′(t) if |k − k′| N0.”
• Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws (2012, methodology): “To show the existence of solution V̂ (t, x), we use the classical Friedrichs’ regularization method, which was used in [7] for example.”
• A note on the Cauchy problem of the Novikov equation (2013, unknown): “3 [31] Assume that p, r2 [1,1], the following estimates hold: (i) If s4 0, kuvkBsp,r cðk f kBsp,rk gkL1 þ k f kL1k gkBsp,r Þ: (ii) If s1 1/p, s2> 1/p (s2 1/p if r1⁄4 1) and s1þ s2> 0.”