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

Debdeep Bhattacharya ()
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Debdeep Bhattacharya: Louisiana State University

Partial Differential Equations and Applications, 2021, vol. 2, issue 6, 1-29

Abstract: Abstract We consider the focusing modified Zakharov–Kuznetsov (mZK) equation in two space dimensions. We prove that solutions which blow up in finite time in the $$H^1(\mathbb {R}^{2})$$ H 1 ( R 2 ) norm have the property that they concentrate a non-trivial portion of their mass (more precisely, at least the amount equal to the mass of the ground state) at the blow-up time. For finite-time blow-up solutions in the $$H^s(\mathbb {R}^2)$$ H s ( R 2 ) norm for $$\frac{17}{18}

Keywords: Modified Zakharov–Kuznetsov equation; Mass-concentration; I-method; Blow-up; 35Q53; 35B44; 37K40; 35C07; 37L50 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00139-y

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