# Mathematics Colloquia and Seminars

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### On one-dimensional semi-linear wave equations with null conditions

**PDE and Applied Math Seminar**

Speaker: | Kevin Luli, UC Davis |

Location: | 3106 MSB |

Start time: | Thu, Jan 11 2018, 2:10PM |

It is well-known that in dimensions at least three, semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such results still hold for a certain class of quasi-linear wave equations with null conditions. The proofs are based on the decay mechanism of linear waves. However, in one dimension, waves do not decay. Nevertheless, we will prove that small data still lead to global solutions if the null condition is satisfied. This is a joint work with S. Yang and P. Yu