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Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential

  • * Corresponding author: Luigi Forcella

    * Corresponding author: Luigi Forcella 
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  • We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.

    Mathematics Subject Classification: Primary: 35Q40; Secondary: 35Q55.


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