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Smooth solution of the generalized system of ferro-magnetic chain

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  • In this paper, we consider the initial value problem with periodic boundary condition for a class of general systems of the ferromagnetic chain

    $z_t=-\alpha z\times (z\times z_{x x})+ z\times z_{x x}+z\times f(z), \qquad (\alpha \geq 0).$

    The existence of unique smooth solutions is proved by using the technique of spatial difference and a priori estimates of higher-order derivatives in Sobolev spaces.

    Mathematics Subject Classification: 35D10, 35Q80.


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