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By using an idea of localized Galilean boost, we show that the data-to-solution map for incompressible Euler equations is not uniformly continuous in $${H^s({\mathbb{R}}^d)}$$Hs(Rd), $${s \ge 0}$$s≥0. This settles the… Click to show full abstract
By using an idea of localized Galilean boost, we show that the data-to-solution map for incompressible Euler equations is not uniformly continuous in $${H^s({\mathbb{R}}^d)}$$Hs(Rd), $${s \ge 0}$$s≥0. This settles the end-point case (s = 0) left open in Himonas–Misiołek (Commun Math Phys 296(1):285–301, 2010) and gives a unified treatment for all Hs. We also show the solution map is nowhere uniformly continuous.
Keywords:
non uniform;
boost non;
galilean boost;
incompressible euler
Journal Title: Communications in Mathematical Physics
Year Published: 2019
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Journal Title: Communications in Mathematical Physics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!