Existence of finite-time splash singularity for a collapsing bubble in Navier-Stokes free boundary problem with surface tension, via δ-wing domain construction.
cc/paper_files/paper/2022/file/ 08342dc6ab69f23167b4123086ad4d38-Paper-Conference
16 Pith papers cite this work. Polarity classification is still indexing.
16
Pith papers citing it
citation-role summary
background 2
extension 1
citation-polarity summary
representative citing papers
Establishes tame weighted Sobolev estimates for linear waves on dynamical asymptotically flat spacetimes settling to Kerr, handling zero-energy bound states via microlocal and energy methods to enable nonlinear global existence results.
Under a fixed scale-invariant bound on suitable weak solutions of 3D Navier-Stokes, smallness of the vertical velocity component yields a positive lower bound on the local regularity radius via harmonic pressure approximation.
For the Benjamin-Ono equation, the leading long-time term with x = O(t^{1/2}) is an explicit universal profile obtained from linearizing the self-similar profile equation, for rational initial data with generic reflection coefficient behavior at the origin.
Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
Mode stability without symmetry assumptions is proved for self-similar wave map blowups in all dimensions d ≥ 4.
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
Introduces Wasserstein Tangential PCA (WT-PCA) as a variational dynamical approach to log-PCA on the Wasserstein space and derives its empirical statistical convergence rate in 2-Wasserstein distance.
Conditional KRR reduces to KRR on a residual kernel with an added O(1/sqrt(N)) term in expected test risk and outperforms standard KRR when the F-component is dominant.
Strictly stable free-boundary minimal hypersurfaces are unique local mass minimizers among relative cycles in small neighborhoods.
Comet-type periodic orbits exist in the CR3BP and undergo vertical self-resonant bifurcations up to multiplicity six in the Earth-Moon system.
Proposes six variants of individual minima-informed DM for MOMPC, including two novel ones, and embeds them in a stabilizing framework with a less restrictive descent condition than prior work.
Solitons from the KdV equation yield reflectionless potentials that approximate confining forces between quarks in spectra and enable tests of flavor-independent interactions.
Continued AI scaling remains feasible only if efficiency doublings recur repeatedly to keep logical compute affordable.
The survey organizes topological methods for counting solutions to Allen-Cahn equations and systems, connecting them to minimal hypersurfaces and multi-phase isoperimetric problems via Gamma-convergence.
citing papers explorer
-
On existence of a collapsed bubble with surface tension in viscous incompressible fluid
Existence of finite-time splash singularity for a collapsing bubble in Navier-Stokes free boundary problem with surface tension, via δ-wing domain construction.
-
(Non-)Linear waves on asymptotically flat spacetimes. II: trapping, bound states, nonlinear applications
Establishes tame weighted Sobolev estimates for linear waves on dynamical asymptotically flat spacetimes settling to Kerr, handling zero-energy bound states via microlocal and energy methods to enable nonlinear global existence results.
-
Finite-Scale One-Component Regularity via Harmonic Pressure for the 3D Navier-Stokes Equations
Under a fixed scale-invariant bound on suitable weak solutions of 3D Navier-Stokes, smallness of the vertical velocity component yields a positive lower bound on the local regularity radius via harmonic pressure approximation.
-
The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality
For the Benjamin-Ono equation, the leading long-time term with x = O(t^{1/2}) is an explicit universal profile obtained from linearizing the self-similar profile equation, for rational initial data with generic reflection coefficient behavior at the origin.
-
Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System
Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
-
Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
-
Mode stability of self-similar wave maps without symmetry in higher dimensions
Mode stability without symmetry assumptions is proved for self-similar wave map blowups in all dimensions d ≥ 4.
-
$\Gamma$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
-
Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergence
Introduces Wasserstein Tangential PCA (WT-PCA) as a variational dynamical approach to log-PCA on the Wasserstein space and derives its empirical statistical convergence rate in 2-Wasserstein distance.
-
Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholding
Conditional KRR reduces to KRR on a residual kernel with an added O(1/sqrt(N)) term in expected test risk and outperforms standard KRR when the F-component is dominant.
-
A Local Minimizing Property of Strictly Stable Free Boundary Minimal Hypersurfaces
Strictly stable free-boundary minimal hypersurfaces are unique local mass minimizers among relative cycles in small neighborhoods.
-
Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization
Proposes six variants of individual minima-informed DM for MOMPC, including two novel ones, and embeds them in a stabilizing framework with a less restrictive descent condition than prior work.
-
From the Great Wave of Translation to the Force between Quarks
Solitons from the KdV equation yield reflectionless potentials that approximate confining forces between quarks in spectra and enable tests of flavor-independent interactions.
-
Continued AI Scaling Requires Repeated Efficiency Doublings
Continued AI scaling remains feasible only if efficiency doublings recur repeatedly to keep logical compute affordable.
-
Survey on topological methods for Allen--Cahn equations and systems
The survey organizes topological methods for counting solutions to Allen-Cahn equations and systems, connecting them to minimal hypersurfaces and multi-phase isoperimetric problems via Gamma-convergence.