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Autor:
Jo, Min Jun
We provide an improved upper bound on the box-counting dimension of the set of potential singular points in suitable weak solutions to the $\alpha$-fractional Navier-Stokes equations for the hyperdissipation case $1<\alpha<\frac{5}{4}$.
Externí odkaz:
http://arxiv.org/abs/2211.15274
Autor:
Jo, Min Jun, Kim, Junha
We give a vorticity-dynamical proof of $C^1\cap H^2$-illposedness of the 2D Euler equations. Our construction shows that the unique Yudovich solution escapes both $C^1$ and $H^2$ instantaneously.
Externí odkaz:
http://arxiv.org/abs/2211.13872
Autor:
Jo, Min Jun, Kim, Junha
We analyze the asymptotic stability of the quasi-linearly stratified densities in the 2D inviscid incompressible porous medium equation on $\bbR^2$ with respect to the buoyancy frequency $N$. Our target density of stratification is the sum of the lar
Externí odkaz:
http://arxiv.org/abs/2210.11437
We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this end, we newly design a normal mode method of effectively leveraging the
Externí odkaz:
http://arxiv.org/abs/2210.10283
The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such approximati
Externí odkaz:
http://arxiv.org/abs/2209.02634
Akademický článek
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Autor:
Jo, Min Jun
Inviscid damping phenomena in mathematical fluid dynamics have been intensively studied for the last decade, as the hydrodynamic analogue of Landau damping for the Vlasov equations. In its full generality, inviscid damping accounts for the extra stab
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::134fae9d2ffbed6288e01bf7d94ebcd4
We prove that the solution of the 3D inviscid Boussinesq equations converges to the solution of the quasi-geostrophic (QG) equations in an asymptotic regime where the intensities of rotation and stratification increase to infinity while the rotation-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6f09412a013a120fdad400cee64b41a
http://arxiv.org/abs/2209.02634
http://arxiv.org/abs/2209.02634