$$L^\infty $$ Ill-Posedness for a Class of Equations Arising in Hydrodynamics
Sign Up to like & getrecommendations! Published in 2019 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-019-01457-7
Abstract: We give a new approach to studying norm inflation (in some critical spaces) for a wide class of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of the n-dimensional Euler equations in… read more here.
Keywords: arising hydrodynamics; class; class equations; equations arising ... See more keywords
Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics
Sign Up to like & getrecommendations! Published in 2021 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.108057
Abstract: Abstract. In dimension n “ 2 and 3, we show that for any initial datum belonging to a dense subset of the energy space, there exist infinitely many global-in-time admissible weak solutions to the isentropic… read more here.
Keywords: dense set; system; set initial; global ill ... See more keywords
Ill-posedness of the stationary Navier-Stokes equations in Besov spaces
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.03.046
Abstract: Abstract The solutions of the stationary Navier-Stokes equations in R n for n ≥ 3 in the scaling invariant Besov spaces are investigated. It is proved that a sequence of bounded smooth external forces whose… read more here.
Keywords: stokes equations; besov spaces; ill posedness; navier stokes ... See more keywords
An efficient method to reduce ill-posedness for structural dynamic load identification
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DOI: 10.1016/j.ymssp.2017.03.039
Abstract: Abstract For the inverse problem of structural dynamic load identification, high system ill-posedness is a main cause leading to instability and low accuracy. In this study, an efficient interpolation-based method is proposed to reduce ill-posedness… read more here.
Keywords: load identification; method; ill posedness; function ... 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