Fourier Analysis and Nonlinear Partial Differential Equations

By H. Bahouri, Jean-Yves Chemin, Raphaël Danchin. 2011

3,157 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/24446ed4c3d12341406b213e58136ad54c706d69

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In Applied Mathematics

1. Nader Masmoudi
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Citations in the corpus

• Landau Damping: Paraproducts and Gevrey Regularity (2013, methodology): “3 The Paraproduct Decomposition Another key Fourier analysis tool employed in this work is the paraproduct decomposition, introduced by Bony [15] (see also [5]).”
• Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces (2013, methodology): “Alternatively one can pose assumptions (at the level of velocity) for u0 or make use of Besov spaces such as in [3].”
• A Lagrangian Approach for the Incompressible Navier‐Stokes Equations with Variable Density (2011, background): “embeds in M(Ḃ n/p−1 p,1 ), a consequence of basic continuity results for the paraproduct operator (see [4]).”
• Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, background): “One may refer to [2,14] for more details.”
• Lectures on singular stochastic PDEs (2015, background): “Dyadic partitions of unity exist, see [1].”
• Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids (2010, background): “(the reader may consult [3], Chap 10 too).”
• On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces (2014, background): “For the proofs of the following propositions, see [1, 10,11,17] and the references therein.”
• The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces (2011, background): “100 in [1] ensures that ∥∥(2js∥∥[u · ∇, j ]q∥∥L∞)j∥∥ r C(‖∇u‖L∞‖q‖Bs ∞,r + ‖∇q‖L∞‖∇u‖Bs−1 ∞,r ).”
• Loss of Regularity for the Continuity Equation with Non-Lipschitz Velocity Field (2018, background): “, with a modulus of continuity satisfying the Osgood condition) are collected for instance in [5].”
• Local existence for the non-resistive MHD equations in Besov spaces (2015, background): “For that reason, we focus mainly on homogeneous Besov spaces; most of the following results have inhomogeneous versions, which can be found in Sections 2.7 and 2.8 of Bahouri et al. (2011).”
• Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems (2020, background): “The following theory of distributions, Fourier analysis and Sobolev spaces can be found in many books (see for example [1, 4, 6, 38, 39, 57, 59, 78, 82]).”
• Well-posedness of a 3D parabolic–hyperbolic Keller–Segel system in the Sobolev space framework (2012, methodology): “1 of [1] by using Littlewood-Paley decomposition, while the third inequality is also a direct consequence of Sobolev embedding theorem.”
• KPZ Reloaded (2015, background): “2 in [BCD11], it suffices to show that max k=0,1,2 sup x∈R |Dψε(x)|t|x|6 C <∞, uniformly in ε ∈ (0, 1].”