Galilean Boost and Non-uniform Continuity for Incompressible Euler
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03373-z
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… read more here.
Keywords: non uniform; boost non; galilean boost; incompressible euler ... See more keywords
Convergence of the three-dimensional compressible Navier-Stokes-Poisson-Korteweg equation to the incompressible Euler equation
Sign Up to like & getrecommendations! Published in 2017 at "Wuhan University Journal of Natural Sciences"
DOI: 10.1007/s11859-017-1212-y
Abstract: We study the combination of quasi-neutral limit and viscosity limit of smooth solution for the three-dimensional compressible viscous Navier-Stokes-Poisson-Korteweg equation for plasmas and semiconductors. When the Debye length and viscosity coefficients are sufficiently small, the… read more here.
Keywords: three dimensional; stokes poisson; incompressible euler; equation ... See more keywords
The incompressible Euler equations under octahedral symmetry: Singularity formation in a fundamental domain
Sign Up to like & getrecommendations! Published in 2021 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.108091
Abstract: We consider the 3D incompressible Euler equations in vorticity form in the following fundamental domain for the octahedral symmetry group: $\{ (x_1,x_2,x_3): 0 read more here.
Keywords: singularity formation; euler equations; incompressible euler;
Global well-posedness of the free-surface incompressible Euler equations with damping
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.02.002
Abstract: Abstract We consider a layer of an incompressible inviscid fluid, bounded below by a fixed solid boundary and above by a free moving boundary, in a horizontally periodic setting. The fluid dynamics is governed by… read more here.
Keywords: incompressible euler; surface; equations damping; free surface ... See more keywords
Strong Ill-Posedness of the 3D Incompressible Euler Equation in Borderline Spaces
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DOI: 10.1093/imrn/rnz158
Abstract: For the $d$-dimensional incompressible Euler equation, the usual energy method gives local well-posedness for initial velocity in Sobolev space $H^s(\mathbb{R}^d)$, $s>s_c:=d/2+1$. The borderline case $s=s_c$ was a folklore conjecture. In the previous paper [2], we… read more here.
Keywords: incompressible euler; strong ill; euler equation; borderline ... See more keywords
Positivity for the curvature of the diffeomorphism group corresponding to the incompressible Euler equation with Coriolis force
Sign Up to like & getrecommendations! Published in 2021 at "Progress of Theoretical and Experimental Physics"
DOI: 10.1093/ptep/ptab043
Abstract: We investigate the geometry of the central extension D̂µ(S2) of the group of volume-preserving diffeomorphisms of the 2-sphere equipped with an L2-metric, for which geodesics correspond to solutions of the incompressible Euler equation with Coriolis… read more here.
Keywords: incompressible euler; euler equation; positivity; coriolis force ... See more keywords
Chaotic Blowup in the 3D Incompressible Euler Equations on a Logarithmic Lattice.
Sign Up to like & getrecommendations! Published in 2018 at "Physical review letters"
DOI: 10.1103/physrevlett.121.064501
Abstract: The dispute on whether the three-dimensional (3D) incompressible Euler equations develop an infinitely large vorticity in a finite time (blowup) keeps increasing due to ambiguous results from state-of-the-art direct numerical simulations (DNS), while the available… read more here.
Keywords: euler; euler equations; incompressible euler; logarithmic lattice ... See more keywords