Siran Li

activity

20162023

most citedOn one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains

28 citations · 97 across the 35 of their papers we have counts for

collaborators

35 papers

math.AP2023★ 2 cited

Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model

Siran Li, Jianing Yang

In this paper, a novel observation is made on a one-dimensional compressible Navier--Stokes model for the dynamic combustion of a reacting mixture of $γ$ -law gases ( $γ > 1$ ) with dis…

math.DG2023

A wedge product theorem of compensated compactness theory with critical exponents on Riemannian manifolds

Xiaojin Bai, Siran Li, Xiangxiang Su

We formulate and prove compensated compactness theorems concerning the limiting behaviour of wedge products of weakly convergent differential forms on closed Riemannian manifolds à…

math.PR2023

Small mass limit of expected signature for physical Brownian motion

Siran Li, Hao Ni, Qianyu Zhu

Physical Brownian motion describes the dynamics of a Brownian particle experiencing frictional force. It was investigated in the classical work [L. S. Ornstein and G. E. Uhlenbeck,…

math.DG2023★ 4 cited

Gaussian kernels on non-simply-connected closed Riemannian manifolds are never positive definite

Siran Li

We show that the Gaussian kernel $exp {- λ d_{g}^{2} (∙, ∙)}$ on any non-simply-connected closed Riemannian manifold $(M, g)$ , where $d_{g}$ is the geodesi…

math.AP2022

On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity

Siran Li

We study the exponential map of group of volume-preserving diffeomorphisms on closed orientable surfaces via the vorticity formulation of the incompressible Euler equation. We pres…

cs.LG2022

Path Development Network with Finite-dimensional Lie Group Representation

Hang Lou, Siran Li, Hao Ni

Signature, lying at the heart of rough path theory, is a central tool for analysing controlled differential equations driven by irregular paths. Recently it has also found extensiv…

math.AP2021★ 6 cited

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…

math.AP2021★ 1 cited

Fractional Sobolev isometric immersions of planar domains

Siran Li, Mohammad Reza Pakzad, Armin Schikorra

We discuss $C^{1}$ regularity and developability of isometric immersions of flat domains into $R^{3}$ enjoying a local fractional Sobolev $W^{1 + s, \frac{2}{s}}$ regularity for $2/3…

math.AP2020

A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa

Siran Li

Let $(M, g_{0})$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces…

math.PR2020

Expected signature of stopped Brownian motion on $d$ -dimensional $C^{2, α}$ -domains has finite radius of convergence everywhere: $2 \leq d \leq 8$

Siran Li, Hao Ni

A fundamental question in rough path theory is whether the expected signature of a geometric rough path completely determines the law of signature. One sufficient condition is that…

math.DG2020

Smoothability of $L^{p}$ -connections on bundles and isometric immersions with $W^{2, p}$ -regularity

Siran Li

We are concerned with two interrelated problems: smoothability of connection 1-forms with low regularity on bundles with prescribed smooth curvature 2-forms, and existence of isome…

math.DG2020

A dynamical--topological obstruction for smooth isometric embeddings of Riemannian manifolds via incompressible Euler equations

Siran Li

We obtain a dynamical--topological obstruction for the existence of isometric embedding of a Riemannian manifold-with-boundary $(M, g)$ : if the first real homology of $M$ is nontriv…

math.HO2020

Volume decay and concentration of high-dimensional Euclidean balls -- a PDE and variational perspective

Siran Li

It is a well-known fact -- which can be shown by elementary calculus -- that the volume of the unit ball in $R^{n}$ decays to zero and simultaneously gets concentrated on th…

math.DG2020★ 1 cited

The Weyl problem of isometric immersions revisited

Siran Li

We revisit the classical problem due to Weyl, as well as its generalisations, concerning the isometric immersions of $S^{2}$ into simply-connected $3$ -dimensional Riemannian…

math.DG2020

Optimal regularity for the Pfaff system and isometric immersions in arbitrary dimensions

Siran Li

We prove the existence, uniqueness, and $W^{1, 2}$ -regularity for the solution to the Pfaff system with antisymmetric $L^{2}$ -coefficient matrix in arbitrary dimensions. Hence, we est…

math.AP2019

A Note on Alberti's Luzin-Type Theorem for Gradients

Siran Li

We give a "soft" proof of Alberti's Luzin-type theorem in [1] (G. Alberti, A Lusintype theorem for gradients, J. Funct. Anal. 100 (1991)), using elementary geometric measure theory…

math.AP2019★ 2 cited

$W^{s, \frac{n}{s}}$ -maps with positive distributional Jacobians

Siran Li, Armin Schikorra

We extend the well-known result that any $f \in W^{1, n} (Ω, R^{n})$ , $Ω \subset R^{n}$ with strictly positive Jacobian is actually continuous: it is also true for fracti…

math.AP2019

Towards a Theory of Multi-Parameter Geometrical Variational Problems: Fibre Bundles, Differential Forms and Riemannian Quasiconvexity

Siran Li

We are concerned with the relaxation and existence theories of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre…

math.DG2019★ 5 cited

Weak Continuity of the Cartan Structural System and Compensated Compactness on Semi-Riemannian Manifolds with Lower Regularity

Gui-Qiang G. Chen, Siran Li

We are concerned with the global weak continuity of the Cartan structural system -- or equivalently, the Gauss--Codazzi--Ricci system -- on semi-Riemannian manifolds with lower reg…

math.DG2019★ 1 cited

Cartan--Whitney Presentation, Non-smooth Analysis and Smoothability of Manifolds: On a theorem of Kondo--Tanaka

Siran Li

Using tools and results from geometric measure theory, we give a simple new proof of the main result (Theorem 1.3) in K. Kondo and M. Tanaka, Approximation of Lipschitz Maps via Im…

math.AP2019★ 1 cited

Counterexamples to the $L^{p}$ -Calderón--Zygmund Estimate on Open Manifolds

Siran Li

Based on a construction due to B. Güneysu and S. Pigola (\textit{Adv. Math.} \textbf{281} (2015), pp.353--393), for each $p \in [1, \infty]$ and $m \in Z_{\geq 2}$ , we exhi…

math.AP2018★ 4 cited

The Inviscid Limit of the Navier-Stokes Equations with Kinematic and Navier Boundary Conditions

Gui-Qiang G. Chen, Siran Li, Zhongmin Qian

We are concerned with the inviscid limit of the Navier-Stokes equations on bounded regular domains in $R^{3}$ with the kinematic and Navier boundary conditions. We first est…

math.AP2018★ 1 cited

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…

math.CA2018

A Note on Generic Transversality of Euclidean Submanifolds

Siran Li

In this short note, we establish a quantitative description of the genericity of transversality of $C^{1}$ -submanifolds in $R^{n}$ : Let $Σ \subset R^{n}$ be a $d$ -dimens…

Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model

A wedge product theorem of compensated compactness theory with critical exponents on Riemannian manifolds

Small mass limit of expected signature for physical Brownian motion

Gaussian kernels on non-simply-connected closed Riemannian manifolds are never positive definite

On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity

Path Development Network with Finite-dimensional Lie Group Representation

On Asymptotic Rigidity and Continuity Problems in Nonlinear Elasticity on Manifolds and Hypersurfaces

Fractional Sobolev isometric immersions of planar domains

A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa

Expected signature of stopped Brownian motion on d-dimensional C2,α-domains has finite radius of convergence everywhere: 2≤d≤8

Smoothability of Lp-connections on bundles and isometric immersions with W2,p-regularity

A dynamical--topological obstruction for smooth isometric embeddings of Riemannian manifolds via incompressible Euler equations

Volume decay and concentration of high-dimensional Euclidean balls -- a PDE and variational perspective

The Weyl problem of isometric immersions revisited

Optimal regularity for the Pfaff system and isometric immersions in arbitrary dimensions

A Note on Alberti's Luzin-Type Theorem for Gradients

Ws,sn​-maps with positive distributional Jacobians

Towards a Theory of Multi-Parameter Geometrical Variational Problems: Fibre Bundles, Differential Forms and Riemannian Quasiconvexity

Weak Continuity of the Cartan Structural System and Compensated Compactness on Semi-Riemannian Manifolds with Lower Regularity

Cartan--Whitney Presentation, Non-smooth Analysis and Smoothability of Manifolds: On a theorem of Kondo--Tanaka

Counterexamples to the Lp-Calderón--Zygmund Estimate on Open Manifolds

The Inviscid Limit of the Navier-Stokes Equations with Kinematic and Navier Boundary Conditions

From the Nash--Kuiper Theorem of Isometric Embeddings to the Euler Equations for Steady Fluid Motions: Analogues, Examples, and Extensions

A Note on Generic Transversality of Euclidean Submanifolds

Expected signature of stopped Brownian motion on $d$ -dimensional $C^{2, α}$ -domains has finite radius of convergence everywhere: $2 \leq d \leq 8$

Smoothability of $L^{p}$ -connections on bundles and isometric immersions with $W^{2, p}$ -regularity

$W^{s, \frac{n}{s}}$ -maps with positive distributional Jacobians

Counterexamples to the $L^{p}$ -Calderón--Zygmund Estimate on Open Manifolds