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Explore the global-in-time evolution of irrotational, isentropic, compressible Euler flow in three dimensions through this mathematical research lecture. Examine a broad class of smooth Cauchy data prescribed on an annulus and surrounded by a non-vacuum constant exterior state, without requiring symmetry assumptions. Learn how imposing a sufficient expansion condition on initial data and utilizing the nonlinear structure of Euler equations demonstrates that the first-order transversal derivative of normalized density decays as ⟨t⟩⁻¹ (log⟨t⟩ + 1)⁻¹, provided perturbations from tangential derivatives are controlled through bootstrap arguments. Discover the construction of global exterior solutions, including a general subclass forming rarefaction at null infinity, with results applicable to data of any total energy size without requiring smallness of transversal derivatives of smooth data. Gain insights into advanced fluid dynamics theory and mathematical analysis techniques for compressible flow problems from this presentation by Qian Wang from the University of Oxford at the Institut des Hautes Etudes Scientifiques.
