Asymptotic decay for defocusing semilinear wave equations in R1+1

期刊： ANNALS OF PDE, 2021; 7 (1)

This paper is devoted to the study of asymptotic behaviors of solutions to the one-dimensional defocusing semilinear wave equations. We prove that fin......

On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

期刊： ANNALS OF PDE, 2021; 7 (1)

We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functio......

Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field

期刊： ANNALS OF PDE, 2021; 7 (1)

We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general class of data, in......

Solvability of a Class of Singular Fourth Order Equations of Monge-Ampere Type

期刊： ANNALS OF PDE, 2021; 7 (2)

We study the solvability of the second boundary value problem for a class of highly singular fourth order equations of Monge-Ampere type. They arise i......

Stability of Solitary Waves for the Modified Camassa-Holm Equation

期刊： ANNALS OF PDE, 2021; 7 (2)

We study the stability of smooth and peaked solitary waves to the modified Camassa-Holm equation. This quasilinear equation with cubic nonlinearity is......