The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
Pure Appl
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A coefficient-based unification of two fluid equations yields exact (1+1)D reductions whose apex dynamics blow up in finite time under stated conditional stability assumptions.
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
The paper is a memorial tribute collecting reminiscences of Robert V. Kohn's exemplary life and contributions to mathematics.
citing papers explorer
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A unified Boussinesq--Euler formulation and finite-time blow-up for a Hou--Luo type boundary-jet system
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
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2D inviscid Boussinesq equations and 3D axisymmetric Euler equations: (1) A unification ($Em$), (2) Finite-time blow-up of two unified $(1+1)$D systems rigorously derived from ($Em$)
A coefficient-based unification of two fluid equations yields exact (1+1)D reductions whose apex dynamics blow up in finite time under stated conditional stability assumptions.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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Robert V. Kohn (1953-2026)
The paper is a memorial tribute collecting reminiscences of Robert V. Kohn's exemplary life and contributions to mathematics.