Introduction:
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The more recent advances in the field of Fluid Mechanics, and more generally, of Partial Differential Equations arising from models of Physics and Continuum Mechanics are increasingly featuring, and motivating, novel Harmonic and Fourier analytical tools. A nonexhaustive list of significant examples are the breakthroughs in the circle of problems related to anomalous dissipation and Onsager's conjecture; the well-posedness and regularity results for the surface quasi-geostrophic equation and related problems; the blow-up problem and double exponential growth of Sobolev norms for the two-dimensional Euler system; Euler wellposedness and elliptic regularity theory in nonsmooth domains; Euler equations in mean oscillation spaces; new estimates for linear and multilinear oscillatory integrals and their applications to linear and nonlinear wave and Schrdinger-type equations. The aim of this special session is to provide an opportunity, for specialists of either discipline, of presenting novel results at the boundary between the fields of harmonic analysis and partial differential equations, with particular focus on the theory of fluids, and discussing open questions, possibly sparkling the need for new analytical tools and fostering future collaborations. |
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