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Results tagged with wave-equation
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user 104213
2
votes
0
answers
69
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On Selberg-Tesfahun's null form estimates for Maxwell-Klein-Gordon equations
In the 2010 paper https://arxiv.org/pdf/1001.5373.pdf Selberg & Tesfahun prove finite-energy well posedness for the Maxwell-Klein-Gordon system in Lorenz gauge, that is if the equations on $\mathbb{R} …
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2
votes
1
answer
136
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Maxwell-Klein-Gordon energy estimates in Klainerman and Machedon's 1994 paper
In the 1994 paper On the Maxwell-Klein-Gordon Equation with Finite Energy of Klainerman and Machedon, the proof of Proposition 1.1 contains the following statement. For $\phi$ (the scalar field of) a …
- 914
1
vote
0
answers
96
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criticality for nonlinear wave equations on manifolds
On $\mathbb{R}^{1+n}$, the initial value problem for the homogeneous wave equation
$$ \Box \phi = \partial_t^2 \phi - \Delta_{\mathbb{R}^n} \phi = 0, \\ (\phi, \partial_t \phi)|_{t=0} = (\phi_0, \phi_ …
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