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arXiv · 1710.09346

Almost sure boundedness of iterates for derivative nonlinear wave equations

Sagun Chanillo·Magdalena Czubak·Dana Mendelson·Andrea Nahmod·Gigliola Staffilani
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Abstract

We study nonlinear wave equations on $\mathbb R^{2+1}$ with quadratic derivative nonlinearities, which include in particular nonlinearities exhibiting a null form structure, with random initial data in $H_x^1\times L^2_x$. In contrast to the counterexamples of Zhou \cite{Zhou} and Foschi-Klainerman \cite{FK}, we obtain a uniform time interval $I$ on which the Picard iterates of all orders are almost surely bounded in $C_t(I ; \dot H_x^1)$.

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Sagun Chanillo, Magdalena Czubak, Dana Mendelson, Andrea Nahmod, Gigliola Staffilani. 2017-10-25. Almost sure boundedness of iterates for derivative nonlinear wave equations. https://arxiv.org/abs/1710.09346

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