OOIR: Observatory of International Research

Papers

(The median citation count of Communications in Partial Differential Equations is 1. 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
The mathematical theory of splitting-merging patterns in phase transition dynamics	14
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	13
Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential	12
On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations	11
Shape optimization for nonlocal anisotropic energies	11
Spectral asymptotics for the vectorial damped wave equation	11
Qualitative properties of solutions to a mass-conserving free boundary problem modeling cell polarization	10
Slow periodic homogenization for Hamilton–jacobi equations	10
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection	9
Topological invariants for interface modes	9
Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations	9
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
Nonlinear enhanced dissipation in viscous Burgers type equations II	8
Stability estimates for the holonomy inverse problem	7
Logarithmic Gross-Pitaevskii equation	7
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

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
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
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
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
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
Homogenization of some periodic Hamilton-Jacobi equations with defects	3
Threshold scattering for the 2D radial cubic-quintic NLS	3
On the motion of a small rigid body in a viscous compressible fluid	3
A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation	3
A fractional Hopf Lemma for sign-changing solutions	3
Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit	3
A priori L ^∞ −bound for Ginzburg-Landau energy minimizers with divergence penalization	3
Monotone solutions for mean field games master equations: continuous state space and common noise	3
Strichartz estimates for Maxwell equations in media: the partially anisotropic case	3
Standing waves and global well-posedness for the 2d Hartree equation with a point interaction	3
Initial data identification in space dependent conservation laws and Hamilton-Jacobi equations	3
Steady solutions for the Schrödinger map equation	3
A transmission problem with (p, q)-Laplacian	3
Segregated solutions for nonlinear Schrödinger systems with weak interspecies forces	2
Hexagonal structures in 2D Navier–Stokes flows	2
The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds	2
Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance	2
Weyl formulae for Schrödinger operators with critically singular potentials	2
Fractional Sobolev regularity for fully nonlinear elliptic equations	2
On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case	2
A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients	2
Critical points of Laplace eigenfunctions on polygons	2
On gradient estimates for heat kernels	2
Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations	2
The Poisson equation involving surface measures	2
Convergence toward the steady state of a collisionless gas with Cercignani–Lampis boundary condition	2
Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits	2
On the limiting amplitude principle for the wave equation with variable coefficients	2
Spectral flow for pair compatible equipartitions	2

Propagation of velocity moments and uniqueness for the magnetized Vlasov–Poisson system	2
L²-type Lyapunov functions for hyperbolic scalar conservation laws	2
Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary	2
Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications	2
The convergence rate of p -harmonic to infinity-harmonic functions	2
Quantitative Hardy inequalities for magnetic Hamiltonians	2
Filamentation near Hill’s vortex	1
The Master Equation in a bounded domain with Neumann conditions	1
On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity	1
Erratum to “optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation”	1
Mean field limit for congestion dynamics	1
Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation	1
Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media	1
Magnetic Schrödinger operators and landscape functions	1
Large harmonic functions for fully nonlinear fractional operators	1
Global estimates for the Hartree–Fock–Bogoliubov equations	1
Well-posedness of Hamilton-Jacobi equations in the Wasserstein space: non-convex Hamiltonians and common noise	1
Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion	1
Analysis and mean-field derivation of a porous-medium equation with fractional diffusion	1
Randomized final-state problem for the Zakharov system in dimension three	1
The lifespan of small data solutions for intermediate long wave equation (ILW)	1
Asymptotics and scattering for wave Klein-Gordon systems	1
Inverse problems for third-order nonlinear perturbations of biharmonic operators	1
Analysis of the generalized Aw-Rascle model	1
Asymptotic stability of solutions to the Navier–Stokes–Fourier system driven by inhomogeneous Dirichlet boundary conditions	1
Lipschitz regularity for Poisson equations involving measures supported on C ^1,Dini interfaces	1
Shock interactions for the Burgers-Hilbert equation	1
Dimension reduction techniques in deterministic mean field games	1
Threshold solutions for the 3 d cubic-quintic NLS	1
Dirichlet problem for weakly harmonic maps with rough data	1
Long time existence for a two-dimensional strongly dispersive Boussinesq system	1
Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines	1
Multiple Delaunay ends solutions of the Cahn-Hilliard equation	1
Hyperbolicity, irrationality exponents and the eta invariant	1
Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange	1
Blow up of solutions for a Parabolic-Elliptic chemotaxis system with gradient dependent chemotactic coefficient	1