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We construct a new class of multi-solitary wave solutions for the masscritical two dimensional nonlinear Schrodinger equation (NLS). Given anyinteger K>1, there exists a global (for positive time) solution of (NLS) thatdecomposes asymptotically into a sum of solitary waves centered at the verticesof a K-sided regular polygon and concentrating at a logarithmic rate in largetime. This solution blows up in infinite time with logarithmic rate. Using thepseudo-conformal transform, this yields the first example of solution blowingup in finite time with a rate strictly above the pseudo-conformal one. Suchsolution concentrates K bubbles at a point. These special behaviors are due tostrong interactions between the waves, in contrast with previous works onmulti-solitary waves of (NLS) where interactions do not affect the blow uprate.

Strongly interacting blow up bubbles for the mass critical NLS