scholarly journals On the a priori estimate for solutions of the Cauchy problem for some non-linear wave equations

1962 ◽  
Vol 2 (1) ◽  
pp. 55-60
Author(s):  
Masaya Yamaguti
Keyword(s):  
Cauchy Problem ◽  
Wave Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Linear Wave ◽  
Priori Estimate ◽  
Non Linear ◽  
The Cauchy Problem ◽  
Linear Wave Equations

LOCAL EXISTENCE FOR SEMILINEAR WAVE EQUATIONS AND APPLICATIONS TO YANG–MILLS EQUATIONS

2005 ◽  
Vol 02 (01) ◽  
pp. 61-76
Author(s):  
YUNG-FU FANG
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Nonlinear Term ◽  
A Priori ◽  
Local Existence ◽  
A Priori Estimate ◽  
Linear Wave ◽  
Yang Mills ◽  
Linear Wave Equations ◽  
Local Result

In this work we are concerned with a local existence of certain semi-linear wave equations for which the initial data has minimal regularity. Assuming the initial data are in H1+∊ and H∊ for any ∊ > 0, we prove a local result by using a fixed point argument, the main ingredient being an a priori estimate for the quadratic nonlinear term uDu. The technique applies to the Yang–Mills equations in the Lorentz gauge.

Uniqueness for stochastic non-linear wave equations

2007 ◽  
Vol 67 (12) ◽  
pp. 3287-3310 ◽  
Author(s):  
Martin Ondreját
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations

scholarly journals Non-linear wave equations for free surface flow over a bump

2020 ◽  
Vol 62 (2) ◽  
pp. 159-169
Author(s):  
Shino Sakaguchi ◽  
Keisuke Nakayama ◽  
Thuy Thi Thu Vu ◽  
Katsuaki Komai ◽  
Peter Nielsen
Keyword(s):  
Free Surface ◽  
Wave Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations
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