This volume in the renowned Abel Symposia series contains the peer-reviewed proceedings of the Abel Symposium 2023 on Partial Differential Equations: Waves, Nonlinearities and Nonlocalities, held at Bårdshaug Mansion in Orkanger outside Trondheim, Norway, June 1316, 2023.

Research in nonlinear partial differential equations has been undergoing an intense development, with new phenomena modelled by increasingly complicated systems integrating nonlocal effects, and with the solution of previously unsolved problems, such as the Onsager conjecture. Comprising fifteen articles written by leading researchers, covering a wide range of topics, this book takes readers to the forefront of a highly active subject.

contributions by world-class speakers conference in the reknowned Abel Symposia series reserach results on hot topics

Inhalt

1 Paralinearization of free boundary problems in fluid dynamics.- 2 Stable stratospheric flows.- 3 Nonlinear forward-backward problems.- 4 The BenjaminOno equation on the line: Explicit formula and small dispersion limit.- 5 Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem.- 6 Incompressible limit of porous media equation with chemotaxis and growth.- 7 On a quasi-resonant nonlinear Schrödinger equation on irrational tori.- 8 The global well-posedness conjecture for 1D cubic dispersive equations.- 9 Regularity of trajectories and smooth observables in rough Euler flows.-10 On continuous time bubbling for the harmonic map heat flow in two dimensions.- 11 A Short Primer on the CalogeroMoser Derivative NLS.- 12 Area Variations under pointwise Lagrangian and Legendrian Constraints.- 13 Wave Turbulence: A statistical theory of weakly nonlinear dispersive waves.- 14 Well-posedness and long time behavior of the Euler Alignment System with adaptive communication strength.- 15 The quartic integrability and long time existence of water waves in 2D.