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We consider the focusing modified Zakharov-Kuznetsov (mZK) equation in twospace dimensions. We prove that solutions which blow up in finite time in the$H^1(\R^{2})$ norm have the property that they concentrate a non-trivialportion of their mass (more precisely, at least the amount equal to the mass ofthe ground state) at blow-up time. For finite-time blow-up solutions in the$H^s(\R^2)$ norm for $\frac{17}{18} < s < 1$, we prove a slightly weakerresult. Moreover, we prove that the stronger concentration result can beextended to the range $ \frac{17}{18} < s \le 1$ under an additional assumptionon the upper bound of the blow-up rate of the solution. The main tools usedhere are the $I$-method and a profile decomposition theorem for a boundedfamily of $H^1(\R^{2})$ functions.

Mass-concentration of low-regularity blow-up solutions to the focusing 2D modified Zakharov-Kuznetsov equation