Long time existence of the Boussinesq equation with large initial data in $\mathbb{R}^n$

2021 ◽  
Vol 19 (4) ◽  
pp. 1137-1147
Author(s):  
Guowei Liu ◽  
Wenlong Sun
Keyword(s):  
Initial Data ◽  
Boussinesq Equation ◽  
Large Initial Data ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

scholarly journals A flow method for a generalization of $ L_{p} $ Christofell-Minkowski problem

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Boya Li ◽  
Hongjie Ju ◽  
Yannan Liu
Keyword(s):  
Initial Data ◽  
Curvature Flow ◽  
Minkowski Problem ◽  
Smooth Solutions ◽  
Flow Method ◽  
Long Time Existence ◽  
Long Time ◽  
Anisotropic Curvature ◽  
Time Existence

<p style='text-indent:20px;'>In this paper, a generalitzation of the <inline-formula><tex-math id="M2">\begin{document}$ L_{p} $\end{document}</tex-math></inline-formula>-Christoffel-Minkowski problem is studied. We consider an anisotropic curvature flow and derive the long-time existence of the flow. Then under some initial data, we obtain the existence of smooth solutions to this problem for <inline-formula><tex-math id="M3">\begin{document}$ c = 1 $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Long-Time Existence for Semi-linear Beam Equations on Irrational Tori

2021 ◽  
Author(s):  
Joackim Bernier ◽  
Roberto Feola ◽  
Benoît Grébert ◽  
Felice Iandoli
Keyword(s):  
Long Time Existence ◽  
Beam Equations ◽  
Long Time ◽  
Time Existence

Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in ℝ2

2018 ◽  
Vol 3 (1) ◽  
pp. 14-18 ◽  
Author(s):  
Chun-Chi Lin ◽  
Yang-Kai Lue
Keyword(s):  
Evolution Equation ◽  
Convergent Subsequence ◽  
Second Order ◽  
Plane Curves ◽  
Smooth Solutions ◽  
Fixed Position ◽  
Elastic Curves ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Abstract For any given C2-smooth initial open curves with fixed position and fixed tangent at the boundary points, we obtain the long-time existence of smooth solutions under the second-order evolution of plane curves. Moreover, the asymptotic limit of a convergent subsequence is an inextensible elastica.

scholarly journals Long-time existence of the edge Yamabe flow

2019 ◽  
Vol 71 (2) ◽  
pp. 651-688 ◽  
Author(s):  
Eric BAHUAUD ◽  
Boris VERTMAN
Keyword(s):  
Yamabe Flow ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence
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