scholarly journals Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

2019 ◽  
Vol 12 (4) ◽  
pp. 1023-1048 ◽  
Author(s):  
Benjamin Dodson
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Besov Space ◽  
Well Posedness ◽  
Critical Besov Space

Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type

2020 ◽  
Vol 17 (01) ◽  
pp. 123-139
Author(s):  
Lucas C. F. Ferreira ◽  
Jhean E. Pérez-López
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Besov Spaces ◽  
Wave Equations ◽  
Well Posedness ◽  
Self Similarity ◽  
Semilinear Wave Equations ◽  
Semilinear Wave Equation

We show global-in-time well-posedness and self-similarity for the semilinear wave equation with nonlinearity [Formula: see text] in a time-weighted framework based on the larger family of homogeneous Besov spaces [Formula: see text] for [Formula: see text]. As a consequence, in some cases of the power [Formula: see text], we cover a initial-data class larger than in some previous results. Our approach relies on dispersive-type estimates and a suitable [Formula: see text]-product estimate in Besov spaces.

scholarly journals Well-posedness of Cauchy problem for Landau equation in critical Besov space

2019 ◽  
Vol 12 (4) ◽  
pp. 829-884
Author(s):  
Hongmei Cao ◽  
◽  
Hao-Guang Li ◽  
Chao-Jiang Xu ◽  
Jiang Xu ◽  
...  
Keyword(s):  
Cauchy Problem ◽  
Besov Space ◽  
Landau Equation ◽  
Well Posedness ◽  
Critical Besov Space

Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in .H s × .H s-1, s> 1/2

2018 ◽  
Vol 2019 (21) ◽  
pp. 6797-6817
Author(s):  
Benjamin Dodson
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Three Dimensions ◽  
Well Posedness ◽  
Critical Space ◽  
Initial Value ◽  
Long Time ◽  
Well Posed

Abstract In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $\dot{H}^{1/2} \times \dot{H}^{-1/2}$. We show that if the initial data is radial and lies in $\left (\dot{H}^{s} \times \dot{H}^{s - 1}\right ) \cap \left (\dot{H}^{1/2} \times \dot{H}^{-1/2}\right )$ for some $s> \frac{1}{2}$, then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11].

The dependences on initial data for the b-family equation in critical Besov space

2014 ◽  
Vol 177 (3) ◽  
pp. 471-492 ◽  
Author(s):  
Hao Tang ◽  
Shijie Shi ◽  
Zhengrong Liu
Keyword(s):  
Initial Data ◽  
Besov Space ◽  
Critical Besov Space
Sign in / Sign up

Export Citation Format

Share Document