Singularity formation and global Well-posedness for the generalized Constantin–Lax–Majda equation with dissipation
Jiajie Chen
Abstract
Abstract We study a generalization due to De Gregorio and Wunsch et al of the Constantin–Lax–Majda equation (gCLM) on the real line where H is the Hilbert transform and . We use the method in Chen J et al (2019 (arXiv:1905.06387)) to prove finite time self-similar blowup for a close to and by establishing nonlinear stability of an approximate self-similar profile. For a > −1, we discuss several classes of initial data and establish global well-posedness and an one-point blowup criterion for different initial data. For , we prove global well-posedness for gCLM with critical and supercritical dissipation.
Topics & Concepts
MathematicsSingularityGeneralizationNonlinear systemDissipationMathematical analysisStability (learning theory)Line (geometry)Supercritical fluidHilbert spaceChenApplied mathematicsExponential stabilityHilbert transformConnection (principal bundle)Initial value problemHodographGravitational singularityBilinear interpolationBurgers' equationSolitonDissipative systemSmall dataReal lineAdvanced Mathematical Physics ProblemsNonlinear Waves and SolitonsNavier-Stokes equation solutions