6 citations · 37 across the 17 of their papers we have counts for
18 papers
On a generalized incompressible model in two dimensions
Hantaek Bae, Kyungkeun Kang, James P Kelliher +1
We analyze a generalized incompressible model proposed by Ohkitani [19]. This model is based on the observation that the two-dimensional Burgers' equation can be related to the inc…
Long-time existence for the 2D ideal Boussinesq and the 2D density-dependent Euler equations
Hantaek Bae, Milton Lopes Filho, Anna Mazzucato +1
We establish long-time existence of smooth solutions to the 2D ideal Boussinesq equations and to the 2D non-homogeneous incompressible Euler equations for initial data consisting o…
On the double Beltrami states in Hall magnetohydrodynamics
Hantaek Bae, Kyungkeun Kang, Jaeyong Shin
In this paper, we investigate double Beltrami states in the Hall magnetohydrodynamic (Hall MHD) equations. Initially, we examine the double Beltrami states as a special class of st…
On the regularity of magneto-vorticity field and the global existence for the Hall magnetohydrodynamic equations
Hantaek Bae, Kyungkeun Kang, Jaeyong Shin
In this paper, we investigate the incompressible viscous and resistive Hall magnetohydrodynamic equations (Hall MHD in short). We first study the regularity of the magneto-vorticit…
On the temporal estimates for the incompressible Navier-Stokes equations and the Hall-magnetohydrodynamic equations
Hantaek Bae, Jinwook Jung, Jaeyong Shin
In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak sol…
Global existence and long time behavior of solutions to some Oldroyd type models in hybrid Besov spaces
Hantaek Bae, Jaeyong Shin
In this paper, we deal with some Oldroyd type models, which describe incompressible viscoelastic fluids. There are 3 parameters in these models: the viscous coefficient of fluid $ν…
Global solutions to Stokes-Magneto equations with fractional dissipations
Hantaek Bae, Hyunwoo Kwon, Jaeyong Shin
In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in and establish the local and global w…
On the existence and temporal asymptotics of solutions for the two and half dimensional Hall MHD
Hantaek Bae, Kyungkeun Kang
In this paper, we deal with the dimensional Hall MHD by taking the velocity field and the magnetic field of the form $u(t,x,y)=\left(\nabla^{\perp}ϕ(t,x,y),…
Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems
Hantaek Bae, Rafael Granero-Belinchón
In this work we prove that the solution of the Serre-Green-Naghdi equation cannot be globally defined when the interface reaches the impervious bottom tangentially. As a consequenc…
Global existence and exponential decay to equilibrium for DLSS-type equations
Hantaek Bae, Rafael Granero-Belinchón
In this paper, we deal with two logarithmic fourth order differential equations: the extended one-dimensional DLSS equation and its multi-dimensional analog. We show the global exi…
On the local and global existence of solutions to 1D transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider the 1D transport equation with nonlocal velocity field: \begin{equation*}\label{intro eq} \begin{split} &θ_t+uθ_x+νΛ^γθ=0, \\ & u=\mathcal{N}(θ), \end{split} \end{equat…
Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations
Hantaek Bae, Kyungkeun Kang, Seick Kim
We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller-Segel system of porous medium type equations coupled…
Global existence of weak solutions to dissipative transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider 1D dissipative transport equations with nonlocal velocity field: \[ θ_t+uθ_x+δu_{x} θ+Λ^γθ=0, \quad u=\mathcal{N}(θ), \] where is a nonlocal operator give…
Striated Regularity for the Euler Equations
Hantaek Bae, James P. Kelliher
In 1993, Chemin proved that vorticity possessing negative Holder regularity in directions given by a sufficient family of vector fields (striated regularity) maintains such regular…
The vortex patches of Serfati
Hantaek Bae, James P Kelliher
In 1993, two proofs of the persistence of regularity of the boundary of a classical vortex patch for the 2D Euler equations were published, one by Chemin (announced in 1991) the ot…
Global existence for some transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón
In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of an one dimensional model of…
Gevrey regularity for a class of dissipative equations with analytic nonlinearity
Hantaek Bae, Animikh Biswas
In this paper, we establish Gevrey class regularity of solutions to a class of dissipative equations with an analytic nonlinearity in the whole space. This generalizes the results…
Analyticity of the Subcritical and Critical Quasi-Geostrophic equations in Besov Spaces
Hantaek Bae, Animikh Biswas, Eitan Tadmor
We establish analyticity of the subcritical and critical quasi-geostrophic equations in critical Besov spaces. The main method is so-called Gevrey estimates, which is motivated by…