23 citations · 125 across the 24 of their papers we have counts for
25 papers
Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion
Yuanzhen Shao, Gieri Simonett
We study a non-isothermal model for incompressible magnetoviscoelastic fluids in , , coupling the incompressible Navier-Stokes equations with the evolution equ…
The primitive equations on curved surfaces
M. Hieber, Y. Shao, G. Simonett +1
In this paper, we study the primitive equations in a collar neighborhood of a smooth closed hypersurface in . Using the framework of maximal -regularity and the…
Coriolis-driven fluid motion on spherical surfaces
Yuanzhen Shao, Gieri Simonett, Mathias Wilke
We consider the motion of an incompressible viscous fluid on a sphere, incorporating the effects of the Coriolis force. We demonstrate that global solutions exist for any divergenc…
The Navier-Stokes equations on manifolds with boundary
Yuanzhen Shao, Gieri Simonett, Mathias Wilke
We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes e…
Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics
Marcelo M. Disconzi, Yuanzhen Shao
We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems.…
On a thermodynamically consistent model for magnetoviscoelastic fluids in 3D
Hengrong Du, Yuanzhen Shao, Gieri Simonett
We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of t…
Modeling and analysis of ensemble average solvation energy and solute-solvent interfacial fluctuations
Yuanzhen Shao, Zhan Shao, Shan Zhao
ariational implicit solvation models (VISM) have gained extensive popularity in the molecular-level solvation analysis of biological systems due to their cost-effectiveness and sat…
A new approach to constrained total variation solvation models and the study of solute-solvent interface profiles
Zhan Chen, Yuanzhen Shao
In the past decade, variational implicit solvation models (VISM) have achieved great success in solvation energy predictions. However, all existing VISMs in literature lack the uni…
Well-posedness for magnetoviscoelastic fluids in 3D
Hengrong Du, Yuanzhen Shao, Gieri Simonett
We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as a quasilinear parabolic system. Using the theory of maximal -reg…
Maximal -regularity of nonlocal parabolic equations in higher order Bessel potential spaces
Nikolaos Roidos, Yuanzhen Shao
We consider fractional parabolic equations with variable coefficients and establish maximal -regularity in Bessel potential spaces of arbitrary nonnegative order. As an appl…
Functional Inequalities involving Nonlocal Operators on Complete Riemannian Manifolds and Their Applications to The Fractional Porous Medium Equation
Nikolaos Roidos, Yuanzhen Shao
The objective of this paper is twofold. First, we conduct a careful study of various functional inequalities involving the fractional Laplacian operators, including nonlocal Sobole…
Local well-posedness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics
Fabio S. Bemfica, Marcelo M. Disconzi, Casey Rodriguez +1
In this manuscript, we study the theory of conformal relativistic viscous hydrodynamics introduced in arXiv:1708.06255, which provided a causal and stable first-order theory of rel…
The fractional porous medium equation on manifolds with conical singularities II
Nikolaos Roidos, Yuanzhen Shao
This is the second of a series of two papers which studies the fractional porous medium equation, with and , posed on a Rie…
The fractional porous medium equation on manifolds with conical singularities I
Nikolaos Roidos, Yuanzhen Shao
This is the first of a series of two papers which studies the fractional porous medium equation on a Riemannian manifold with isolated conical singularities. In this article, we sh…
The harmonic map heat flow on conic manifolds
Yuanzhen Shao, Changyou Wang
In this article, we study the the harmonic map heat flow from a manifold with conic singularities to a closed manifold. In particular, we have proved the short time existence and u…
Global solutions to the Porous medium equations on singular manifolds
Yuanzhen Shao
The main objective of the present work is to discuss the global existence and stability of solutions to the porous medium equations on Riemannian manifolds with singularities. Seve…
Wellposedness of a nonlocal nonlinear diffusion equation of image processing
Patrick Guidotti, Yuanzhen Shao
Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data. The resul…
The Yamabe flow on incomplete manifolds
Yuanzhen Shao
This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-fr…
Singular parabolic equations of second order on manifolds with singularities
Yuanzhen Shao
The main aim of this article is to establish an -theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein…
On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem with surface tension
Jan Pruess, Yuanzhen Shao, Gieri Simonett
We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent dif…
Some Remarks on Uniformly Regular Riemannian Manifolds
Marcelo Disconzi, Yuanzhen Shao, Gieri Simonett
We establish the equivalence between the family of closed uniformly regular Riemannian manifolds and the class of complete manifolds with bounded geometry.
Continuous maximal regularity on singular manifolds and its applications
Yuanzhen Shao
In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate…
A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows
Yuanzhen Shao
It is the purpose of this article to establish a technical tool to study regularity of solutions to parabolic equations on manifolds. As applications of this technique, we prove th…
Continuous maximal regularity on uniformly regular Riemannian manifolds
Yuanzhen Shao, Gieri Simonett
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show tha…