34 citations · 94 across the 14 of their papers we have counts for
14 papers
Non-Uniqueness in Plane Fluid Flows
Heiko Gimperlein, Michael Grinfeld, Robin J. Knops +1
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a sing…
Existence, uniqueness, and long-time behavior of linearized field dislocation dynamics
Amit Acharya, Marshall Slemrod
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state o…
On Asymptotic Rigidity and Continuity Problems in Nonlinear Elasticity on Manifolds and Hypersurfaces
Gui-Qiang G. Chen, Siran Li, Marshall Slemrod
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this…
From the Nash--Kuiper Theorem of Isometric Embeddings to the Euler Equations for Steady Fluid Motions: Analogues, Examples, and Extensions
Siran Li, Marshall Slemrod
Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface…
Fluids, Geometry, and the Onset of Navier-Stokes Turbulence in Three Space Dimensions
Gui-Qiang G. Chen, Marshall Slemrod, Dehua Wang
A theory for the evolution of a metric driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an e…
Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions
Amit Acharya, Gui-Qiang Chen, Siran Li +2
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonl…