2 citations · 2 across the 4 of their papers we have counts for
5 papers
Remarks on the convex integration technique applied to singular stochastic partial differential equations
Hongjie Dong, Kazuo Yamazaki
Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms…
-estimates for nonlocal equations with general Lévy measures
Hongjie Dong, Junhee Ryu
We consider nonlocal operators of the form \begin{equation*} L_t u(x) = \int_{\mathbb{R}^d} \left( u(x+y)-u(x)-\nabla u(x)\cdot y^{(σ)} \right) ν_t(dy), \end{equation*} where …
-estimates of the conormal derivative problem for parabolic equations with time measurable coefficients and -weights
Hongjie Dong, Pilgyu Jung, Doyoon Kim
This paper investigates weighted mixed-norm estimates for divergence-type parabolic equations on Reifenberg-flat domains with the conormal derivative boundary condition. The leadin…
Global well-posedness for supercritical SQG with perturbations of radially symmetric data
Aynur Bulut, Hongjie Dong
We study the global well-posedness of the supercritical dissipative surface quasi-geostrophic (SQG) equation, a key model in geophysical fluid dynamics. While local well-posedness…
On the existence of smooth solutions for fully nonlinear parabolic equations with measurable "coefficients" without convexity assumptions
Hongjie Dong, Nicolai V. Krylov
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in any cylindrical smooth domain with…