Vlasov-Poisson equation in weighted Sobolev space Wm,p(w)

• Autores: Cong He, Jingchun Chen
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 2, 2022, págs. 211-226
• Idioma: inglés
• DOI: 10.56754/0719-0646.2402.0211
• Enlaces
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• Resumen
  • español

    RESUMEN En este artículo, estamos interesados en que la ecuación de Vlasov-Poisson está bien puesta cercana al vacío en el espacio de Sobolev Wm,p(w) con peso. La parte más difícil proviene de estimaciones del término electrónico ∇xϕ. Para superar esta dificultad, establecemos las estimaciones Lp-Lq del término electrónico ∇xϕ; donde algún peso es también introducido para obtener la estimación fuera de la diagonal. El peso es también útil cuando se trata de controlar el término de la derivada de alto orden.

  • English

    ABSTRACT In this paper, we are concerned about the well-posedness of Vlasov-Poisson equation near vaccum in weighted Sobolev space Wm,p(w). The most difficult part comes from estimates of the electronic term ∇xϕ. To overcome this difficulty, we establish the Lp-Lq estimates of the electronic term ∇xϕ; some weight is introduced as well to obtain the off-diagonal estimate. The weight is also useful when it comes to control the higher-order derivative term.

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