Nonlinear Schrodinger Equations at Critical Regularity

By Rowan Killip, M. Vi. 2013

263 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c2000ee294bb12d27d435c2a275c631cee701438

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Citations in the corpus

Maximizers for the Stein–Tomas Inequality (2016, unknown): “4 with T (−∆) replaced by −∆/2 is essentially due to [34] and appears in a slightly stronger form in [22].”
Scattering for the radial 3D cubic wave equation (2014, methodology): “This technique was developed by Tao in [47] and utilized in the Kenig-Merle framework for nonlinear Schrödinger problems by Killip and Visan [27, 28, 30], and for semilinear wave equations in [29, 5, 6].”
Continuous dependence for NLS in fractional order spaces (2010, background): “Continuous dependence in H 1(RN) is proved in [12] in the subcritical case (N − 2)α < 4 and in [8,16,22,17] in the critical case (N − 2)α = 4.”
Quintic NLS in the exterior of a strictly convex obstacle (2012, background): “Its predecessor in the Euclidean case can be found in [19]; for versions in higher dimensional Euclidean spaces see [47, 59, 66].”
A refinement of the Strichartz inequality for the wave equation with applications (2012, unknown): “The profile decomposition has traditionally proven useful in the nonlinear theory (see for example [13–15], [16,17], [26], [28], [30–33], [34], [36], [37], [38], [39], [40–42], [48] or [60,61]).”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, background): “Critical mass behavior is also a property of other related critical PDE, such as the marginal unstable thin film equation [63, 7] and critical nonlinear Schrödinger equations [62, 37].”