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Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

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Maria Colombo, Silja Noëmi Aline Haffter
2023

Abstract

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; i0.M0//.

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https://infoscience.epfl.ch/entities/publication/c5d13360-0408-42e3-938a-5a20e934a38a

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In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.

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