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math.AP2025
On the variational dual formulation of the Nash system and an adaptive convex gradient-flow approach to nonlinear PDEs
Dmitry Vorotnikov, Amit Acharya
We investigate the influence of base states on the consistency of the dual variational formulation for quadratic systems of PDEs, which are not necessarily conservative (typical ex…
math.AP2025
Dafermos' principle and Brenier's duality scheme for defocusing dispersive equations
Dmitry Vorotnikov
We discover an abstract structure behind several nonlinear dispersive equations (including the NLS, NLKG and GKdV equations with generic defocusing power-law nonlinearities) that i…