TY - JOUR AU - He, Cong AU - Chen, Jingchun PY - 2022/08/22 Y2 - 2024/03/28 TI - Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\) JF - CUBO, A Mathematical Journal JA - CUBO VL - 24 IS - 2 SE - Articles DO - 10.56754/0719-0646.2402.0211 UR - https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3095 SP - 211–226 AB - <p class="p1">In this paper, we are concerned about the well-posedness of Vlasov-Poisson equation near vaccum in weighted Sobolev space \(W^{m, p}(w)\). The most difficult part comes from estimates of the electronic term \( abla_{x}\phi\). To overcome this difficulty, we establish the \(L^p\)-\(L^q\) estimates of the electronic term \( abla_{x}\phi\); some weight is introduced as well<span class="Apple-converted-space">&nbsp; </span>to obtain the off-diagonal estimate. The weight is also useful when it comes to control the higher-order derivative term.</p> ER -