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- Princeton UniversityUS205 papers
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6 papers · 2 filters
Convex entropy, Hopf bifurcation, and viscous and inviscid shock stability
Blake Barker, Heinrich Freistühler, Kevin Zumbrun
We consider by a combination of analytical and numerical techniques some basic questions regarding the relations between inviscid and viscous stability and existence of a convex en…
On elliptic equations in a half space or in convex wedges with irregular coefficients
Hongjie Dong
We consider second-order elliptic equations in a half space with leading coefficients measurable in a tangential direction. We prove the -estimate and solvability for the Di…
Global solutions to a logarithmically regularized 2D Euler equation
Hongjie Dong, Dong Li
We construct global solutions to a logarithmically modified 2D Euler vorticity equation. Our main tool is a new logarithm interpolation inequality which…
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…
On a family of exact solutions to the incompressible liquid crystals in two dimensions
Hongjie Dong, Zhen Lei
In this paper we construct a family of exact strong solutions to the two-dimensional incompressible liquid crystal equations with finite energy. The initial velocity is chosen to b…
Square function/non-tangential maximal function estimates and the dirichlet problem for non-symmetric elliptic operators
Steve Hofmann, Carlos Kenig, Svitlana Mayboroda +1
We consider divergence form elliptic operators L = - div A(x)\nabla, defined in the half space R^{n+1}_+, n \geq 2, where the coefficient matrix A(x) is bounded, measurable, unifor…