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
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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
Black hole solutions and Euler equation in Rastall and generalized Rastall theories of gravity
Sign Up to like & getrecommendations! Published in 2019 at "Modern Physics Letters A"
DOI: 10.1142/s0217732319503048
Abstract: Focusing on the special case of generalized Rastall theory, as a subclass of the non-minimal curvature-matter coupling theories in which the field equations are mathematically similar to the Einste... read more here.
Keywords: generalized rastall; black hole; euler equation; solutions euler ... See more keywords
Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-Sided Distributions via Laplace Transform
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DOI: 10.3390/math7040376
Abstract: Using the Laplace transform technique, we investigate the generalized solutions of the third-order Cauchy-Euler equation of the form t 3 y ′ ′ ′ ( t ) + a t 2 y ′ ′ (… read more here.
Keywords: solutions third; euler equation; third order;