scholarly journals Long time existence of classical solutions for the 3D incompressible rotating Euler equations

2016 ◽  
Vol 68 (2) ◽  
pp. 579-608 ◽  
Author(s):  
Ryo TAKADA
Keyword(s):  
Euler Equations ◽  
Classical Solutions ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Long-time existence of classical solutions to a one-dimensional swelling gel

2014 ◽  
Vol 25 (01) ◽  
pp. 165-194 ◽  
Author(s):  
M. Carme Calderer ◽  
Robin Ming Chen
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Lagrangian Formulation ◽  
Classical Solutions ◽  
Governing Equations ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

In this paper, we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a mass-Lagrangian formulation, the free boundary is transformed into a fixed boundary. We prove the existence of long-time C1-solutions to the transformed fixed boundary problem.

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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