18 citations · 44 across the 13 of their papers we have counts for
13 papers
Keller-Segel-Navier-Stokes systems involving general sensitivities with Signal-Dependent Power-Law Decay
Jaewook Ahn, Sukjung Hwang
This paper investigates a two-dimensional Keller--Segel--Navier--Stokes system with a tensor-valued chemotactic sensitivity . Under a signal-dependent power-decay conditi…
Existence of weak solutions for fast diffusion equation with a divergence type of drift term
Sukjung Hwang, Kyungkeun Kang, Hwa Kil Kim
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the -energy inequality and speed estimate in Wasserstein s…
Existence of weak solutions for nonlinear drift-diffusion equations with measure data
Sukjung Hwang, Kyungkeun Kang, Hwa Kil Kim +1
We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with measure data. We establish the existence of nonnegative weak soluti…
Existence of weak solutions for Porous medium equation with a divergence type of drift term in a bounded domain
Sukjung Hwang, Kyungkeun Kang, Hwa Kil Kim
We study porous medium equations with a divergence form of drift terms in a bounded domain with no-flux lateral boundary conditions. We establish -weak solutions for $ 1\leq q…
Existence of weak solutions for Porous medium equation with a divergence type of drift term
Sukjung Hwang, Kyungkeun Kang, Haw Kil Kim
We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of -weak solutions (satisfying energy estimates or even furt…
Continuity results for degenerate diffusion equations with drifts
Sukjung Hwang, Yuming Paul Zhang
In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form \[ u_{t} = Δu^{m} + \nabla\cdot \left( B (x,t) \,…
Uniform boundedness for weak solutions of quasilinear parabolic equations
Karthik Adimurthi, Sukjung Hwang
In this paper, we study the boundedness of weak solutions to quasilinear parabolic equations of the form \[u_t - \text{div} \mathcal{A}(x,t,\nabla u) = 0, \] where the nonlinearity…
Parabolic Dirichlet Boundary Value Problem and VMO-type time-varying domains
Martin Dindoš, Luke Dyer, Sukjung Hwang
We prove the solvability of the parabolic Dirichlet boundary value problem for for a PDE of the form $u_t = \mbox{div} (A \nabla u) + B \cdot \nabla u$ on…
Green's function for second order elliptic equations in non-divergence form
Sukjung Hwang, Seick Kim
We construct the Green function for second order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain…
The Dirichlet boundary problem for second order Elliptic Systems with rough coefficients
Martin Dindoš, Marius Mitrea, Sukjung Hwang
Given a domain above a Lipschitz graph, we establish solvability results for strongly elliptic second-order systems in divergence-form, allowed to have lower-order (drift) terms, w…
Holder continuity of Keller-Segel equations of porous medium type coupled to fluid equations
Yun-Sung Chung, Sukjung Hwang, Kyungkeun Kang +1
We consider a coupled system consisting of a degenerate porous medium type of Keller-Segel system and Stokes system modeling the motion of swimming bacteria living in fluid and con…
Hölder continuity of a bounded weak solution of generalized parabolic Laplacian equations
Sukjung Hwang, Gary M. Lieberman
Here we generalize quasilinear parabolic Laplacian type equations to obtain the prototype equation as \[ u_t - \text{div} (g(|Du|)/ |Du| \cdot Du) = 0, \] where a nonnegative,…
The Dirichlet boundary problem for second order parabolic operators satisfying Carleson condition
Martin Dindoš, Sukjung Hwang
We establish , solvability of the Dirichlet boundary value problem for a parabolic equation $u_t-\mbox{div}(A\nabla u)=0$ on time-varying domains with coeffi…