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 2021-02-01 to 2025-02-01.)

Article	Citations
Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory	65
The Hele–Shaw flow as the sharp interface limit of the Cahn–Hilliard equation with disparate mobilities	54
The mathematical theory of splitting-merging patterns in phase transition dynamics	33
Moving planes for domain walls in a coupled system	20
A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation	17
A Globally Stable Self-Similar Blowup Profile in Energy Supercritical Yang-Mills Theory	14
New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data	14
Logarithmic Gross-Pitaevskii equation	14
Quasilinear wave equations on Schwarzschild–de Sitter	13
Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity	12
Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential	11
Spectral asymptotics for the vectorial damped wave equation	10
Inhomogeneous global minimizers to the one-phase free boundary problem	10
Slow periodic homogenization for Hamilton–jacobi equations	9
Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential	9
On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations	9
Unique continuation through hyperplane for higher order parabolic and Schrödinger equations	9
Shape optimization for nonlocal anisotropic energies	9
Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows	8
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ³ nonlinear response	8
Qualitative properties of solutions to a mass-conserving free boundary problem modeling cell polarization	8
Topological invariants for interface modes	7
Nonlinear enhanced dissipation in viscous Burgers type equations II	6
Stability estimates for the holonomy inverse problem	6
Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations	6

Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection	6
Mixed local and nonlocal elliptic operators: regularity and maximum principles	6
Convergence towards equilibrium for a model with partial diffusion	6
Global dynamics of small solutions to the modified fractional Korteweg-de Vries and fractional cubic nonlinear Schrödinger equations	6
Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients	6
Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity	5
Positive solutions to the sublinear Lane-Emden equation are isolated	5
Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity	5
Threshold scattering for the 2D radial cubic-quintic NLS	5
Correction	5
The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds	4
Small data global regularity for half-wave maps in n = 4 dimensions	4
Nodal sets for broken quasilinear partial differential equations with Dini coefficients	4
A transmission problem with (p, q)-Laplacian	4
Lotka–Volterra competition-diffusion system: the critical competition case	4
Taxis-driven persistent localization in a degenerate Keller-Segel system	4
A variational approach to first order kinetic mean field games with local couplings	4
Weak Harnack inequalities for eigenvalues and constant rank theorems	4
Sharp convergence rates for Darcy’s law	4
Erratum: the Poisson equation involving surface measures	4
On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds	4
Stable discontinuous stationary solutions to reaction-diffusion-ODE systems	4
Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations	4
Self-similar behavior of the exchange-driven growth model with product kernel	4