2 problems

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The simple-states conjecture for long-time dynamics of two-dimensional incompressible equations
For a two-dimensional incompressible equation, let a simple state mean a steady state, traveling wave, periodic wave, or quasi-periodic wave. Simple-states conjecture. The long-tim…
Conjecturesolvedincompressible-fluids long-time-dynamics quasi-periodic-wavesarXiv posted 2 days ago
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Convergence of non-dispersive solutions to the stable soliton branch
Consider solutions of the nonlinear Schrödinger equation that do not disperse as $t\rightarrow\infty$ , and let the stable portion of the soliton curve be the region where…
Conjectureopenlong-time-dynamics nonlinear-schrodinger-equations soliton-stabilityarXiv posted 2 days ago

The simple-states conjecture for long-time dynamics of two-dimensional incompressible equations