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7. Landau Equation

    1. Homogeneous relativistic Landau equation

          The homogeneous relativistic Landau equation is given by $$\partial_t f = \mathcal{C}(f,f)$$ where $$C(h,g)(p) : = \partial_{p_i} \int_{\mathbb{R}^3} \Phi^{ij}(p,q)\left\{h(q)\partial_{p_j}g(p) - \partial_{q_j}h(q)g(p)\right\}dq$$ where Einstein summation convention is used.

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      Problem 7.1.

      [Stanley Snelson] Prove global existence of smooth solutions for the relativistic Landau equation.

        • Example of blowup for inhomogeneous Landau (or Boltzmann)


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          Problem 7.2.

          [Jiajie Chen] Can we find a set of conditions such that the homogeneous equation is globally well-posed, but the inhomogeneous equation blows up? Can this be down for the isotropic Landau equation?

              Cite this as: AimPL: Integro-differential equations in many-particle interacting systems, available at http://aimpl.org/manyparticle.