Rough sound waves in \(3D\) compressible Euler flow with vorticity

DOI10.1007/s00029-021-00733-3zbMath1496.35296arXiv1909.02550OpenAlexW2971563739MaRDI QIDQ2071751

Jared Speck, Marcelo M. Disconzi, Chenyun Luo, Giusy Mazzone

Publication date: 31 January 2022

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.02550

zbMATH Keywords

Strichartz estimateeikonal equationshocksSchauder estimatelow regularityRaychaudhuri's equationnull geometryeikonal functionvectorfield method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Shock waves and blast waves in fluid mechanics (76L05) Hydro- and aero-acoustics (76Q05) Second-order hyperbolic equations (35L10) Euler equations (35Q31)

Related Items (6)

Low regularity ill-posedness for non-strictly hyperbolic systems in three dimensions ⋮ WKB analysis of the logarithmic nonlinear Schrödinger equation in an analytic framework ⋮ Low regularity ill-posedness for elastic waves driven by shock formation ⋮ The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in 1D and multi-dimensions ⋮ Local well-posedness of the free-boundary incompressible magnetohydrodynamics with surface tension ⋮ Rough solutions of the 3-D compressible Euler equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates
• On breakdown criteria for nonvacuum Einstein equations
• Sharp counterexamples for Strichartz estimates for low regularity metrics
• Compressible fluid flow and systems of conservation laws in several space variables
• Rough solutions of the Einstein-vacuum equations
• The causal structure of microlocalized rough Einstein metrics
• Sharp local well-posedness results for the nonlinear wave equation
• The bounded \(L^2\) curvature conjecture
• The formation of black holes in general relativity.
• The Cauchy problem in general relativity.
• Pseudodifferential operators and nonlinear PDE
• A parametrix construction for wave equations with \(C^{1,1}\) coefficients
• Counterexamples to local existence for quasilinear wave equations
• Improved local well-posedness for quasilinear wave equations in dimension three
• Elliptic partial differential equations of second order
• Stable big bang formation in near-FLRW solutions to the Einstein-scalar field and Einstein-stiff fluid systems
• The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology \(\mathbb{S}^3\)
• A geometric approach for sharp local well-posedness of quasilinear wave equations
• A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation
• Causal geometry of Einstein-vacuum spacetimes with finite curvature flux
• Shock formation in solutions to the \(2D\) compressible Euler equations in the presence of non-zero vorticity
• A proof of the instability of AdS for the Einstein-null dust system with an inner mirror
• Rough solutions of Einstein vacuum equations in CMCSH gauge
• A new formulation of the \(3D\) compressible Euler equations with dynamic entropy: remarkable null structures and regularity properties
• A proof of Friedman's ergosphere instability for scalar waves
• The relativistic Euler equations: remarkable null structures and regularity properties
• A geometric approach to the Littlewood-Paley theory
• Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, II
• Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III
• Compressible Flow and Euler's Equations
• Causal geometry of rough Einstein CMCSH spacetime
• Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations
• Fourier Analysis and Nonlinear Partial Differential Equations
• Improved breakdown criterion for einstein vacuum equations in CMC gauge
• On the radius of injectivity of null hypersurfaces
• Equations d'ondes quasilineaires et estimations de Strichartz
• Newton polygons as lattice points
• The hidden null structure of the compressible Euler equations and a prelude to applications
• Nonuniqueness of Weak Solutions to the SQG Equation
• Motion of slightly compressible fluids in a bounded domain, II
• The motion of point particles in curved spacetime

This page was built for publication: Rough sound waves in \(3D\) compressible Euler flow with vorticity