4 papers
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…