OOIR: Observatory of International Research

Papers

(The TQCC of Communications in Partial Differential Equations is 4. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-04-01 to 2025-04-01.)

Article	Citations
Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory	82
Spontaneous curvature effects of the Helfrich flow: singularities and convergence	20
Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity	17
The Hele–Shaw flow as the sharp interface limit of the Cahn–Hilliard equation with disparate mobilities	17
A Globally Stable Self-Similar Blowup Profile in Energy Supercritical Yang-Mills Theory	14
The mathematical theory of splitting-merging patterns in phase transition dynamics	14
New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data	13
Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential	12
Spectral asymptotics for the vectorial damped wave equation	11
On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations	11
Shape optimization for nonlocal anisotropic energies	11
Slow periodic homogenization for Hamilton–jacobi equations	10
Qualitative properties of solutions to a mass-conserving free boundary problem modeling cell polarization	10
Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations	9
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection	9
Topological invariants for interface modes	9
Nonlinear enhanced dissipation in viscous Burgers type equations II	8
Inhomogeneous global minimizers to the one-phase free boundary problem	8
Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients	8
Logarithmic Gross-Pitaevskii equation	7
Stability estimates for the holonomy inverse problem	7
Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential	6
Correction	6
Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity	6
Quasilinear wave equations on Schwarzschild–de Sitter	6

Global dynamics of small solutions to the modified fractional Korteweg-de Vries and fractional cubic nonlinear Schrödinger equations	6
Convergence towards equilibrium for a model with partial diffusion	6
Variational interacting particle systems and Vlasov equations	6
A PDE framework of consensus-based optimization for objectives with multiple global minimizers	5
Comparison of viscosity solutions for a class of second-order PDEs on the Wasserstein space	5
Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity	5
Mixed local and nonlocal elliptic operators: regularity and maximum principles	5
Positive solutions to the sublinear Lane-Emden equation are isolated	5
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ³ nonlinear response	5
Sharp convergence rates for Darcy’s law	4
On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds	4
Taxis-driven persistent localization in a degenerate Keller-Segel system	4
Nodal sets for broken quasilinear partial differential equations with Dini coefficients	4
Stable discontinuous stationary solutions to reaction-diffusion-ODE systems	4
Small data global regularity for half-wave maps in n = 4 dimensions	4
Lotka–Volterra competition-diffusion system: the critical competition case	4
A weakly turbulent solution to the cubic nonlinear harmonic oscillator on ℝ ² perturbed by a real smooth potential decaying to zero at infinity	4
Propagation of chaos for the Cucker-Smale systems under heavy tail communication	4
Hyperbolic–parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion	4
Erratum: the Poisson equation involving surface measures	4
A variational approach to first order kinetic mean field games with local couplings	4