Fourier Analysis Methods for PDE's

By Raphaël Danchin. 2005

217 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b1dfef935dc85cbebbe578d06664bd0de329b596

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Citations in the corpus

• Existence and asymptotic behavior of C1 solutions to the multi-dimensional compressible Euler equations with damping (2007, methodology): “(Here, we use the result of continuity for the remainder, see [1] Proposition 1.”
• Global well-posedness for the micropolar fluid system in critical Besov spaces (2010, unknown): “+ × R3), for ε∈ (0,1), the map: (uen,ωen) 7→(χuen,χeωn) is compact from B˙ 3 p −2 p,∞ ∩B˙ 3 p −1−ε p,∞ × B˙ 3 p −1 p,∞ +B˙ 3 p −1−ε p,∞ into B˙ 3 p −2 p,∞ × B˙ 3 p −1 p,∞ +B˙ 3 p −2 p,∞ , see [11]. By applying Ascoli’s theorem and Cantor’s diagonal process, there exists some distribution (eu,eω)”
• Local well-posedness of the viscous surface wave problem without surface tension (2013, result): “Note that the result in [13] is stated for Σ = R2, but the same result holds in the periodic setting Σ = (L1T)× (L2T), as described in [14].”
• The Cauchy problem for the integrable Novikov equation (2012, methodology): “In this paper, motivated by [2,4], by using the Littlewood–Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for (1.”
• Global Existence for the Multi-Dimensional Compressible Viscoelastic flows (2010, methodology): “1) is true modulo polynimials (see [1, 2, 6]).”
• Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension (2013, result): “Note that the result in [9] is stated for Σ = R2, but the same result holds in the periodic setting Σ = (L1T) × (L2T), as described in [10].”
• Decay of viscous surface waves without surface tension (2010, unknown): “Note that the result in [10] is stated for Σ = R(2), but the same result holds in the periodic setting Σ = (L1T)× (L2T), as described in [11].”