Latest Research in Analysis of PDEs

Top Research Topics in Analysis of PDEs

• Analysis of PDEs — 8 papers
• Navier-Stokes equation solutions — 4 papers
• Fluid dynamics and aerodynamics studies — 3 papers
• Probability — 3 papers
• Nonlinear Waves and Solitons — 2 papers
• Numerical Analysis — 2 papers
• Stability and Controllability of Differential Equations — 2 papers
• Nonlinear Dynamics and Pattern Formation — 1 papers
• Plasma Physics — 1 papers
• Mathematical Biology Tumor Growth — 1 papers

Highest-Cited Papers

1. The Cauchy problem of a pressureless two-phase flow system in three-dimensional space
2. Slow-moving pattern interfaces in general directions for a two-dimensional Swift–Hohenberg-type equation
3. On the chaotic behavior of the Lagrangian flow of the 2D Navier-Stokes system with bounded degenerate noise
4. Navier-Stokes Open Problem: No New Math, Only Expository Lectures — E8 Intelligence Research
5. Navier-Stokes Open Problem: No New Math, Only Expository Lectures — E8 Intelligence Research
6. A Structural Dismantling of OpenAI's "Finite‑Time blowup for Navier–Stokes"
7. Entropy stable numerical schemes for divergence diminishing Chew, Goldberger & Low equations for plasma flows
8. Long-time dynamics of stochastic 2D hydrodynamic-type evolution equations driven by multiplicative Lévy noise
9. Renyi's Relative Entropy Lyapunov Functional for Convergence to Invariant Measure in Dissipative Stochastic Hamiltonian Systems
10. Stability of vortex lines attached to airfoils in subsonic Euler flows
11. A symmetric exponential wave integrator for the long-time dynamics of weakly nonlinear Klein–Gordon equation
12. Stable determination of coefficients for the nonlinear third-order acoustic equations
13. Exploration of the 3D Incompressible Euler Equations
14. Systems in Chemotaxis: Mathematical Modeling, Invariant Analysis, Solitons and Numerical Solution
15. Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points
16. Convergence Rate toward Rarefaction Wave under Periodic Perturbation for Generalized Korteweg-de Vries-Burgers equation
17. Moderate Deviations for Nonlinear Hawkes Processes
18. Computing statistical Euler limits of the Navier--Stokes equations in three dimensions
19. Global asymptotic stability of KdV-Burgers fronts in a weakly two-dimensional model
20. An intrinsic expansion approach to the Galerkin approximations for the Navier-Stokes equations (with an appendix by Chengzhang Fu)