Three new results on continuation criteria for the 3D relativistic Vlasov-Maxwell system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Patel, Neel¹ 

[1] Univ Penn, Dept Math, 209 South 33rd St, Philadelphia, PA 19104 USA

关键词: Continuation and prolongation of solutions;    Collisionless Plasmas;    Relativistic Vlasov-Maxwell system;    Well-posedness;    Partial Differential Equations;   

DOI  :  10.1016/j.jde.2017.10.008

来源: Elsevier

【 摘 要 】

We consider continuation criteria for the three-dimensional relativistic Vlasov-Maxwell system. When the particle density, f(t,x,p), is compactly supported at t = 0, we prove parallel to p(18/sr-1+beta)f parallel to(LiLxLp1)-L-infinity-L-r less than or similar to 1, where 1 <= r <= 2 and beta > 0 is arbitrarily small, is a continuation criteria. Our continuation criteria is an improvement in the 1 <= r <= 2 range to the previously best known criteria parallel to p(4/r-1+beta) f parallel to(LtLxLp1)-L-infinity-L-r less than or similar to 1 due to Kunze [7]. We also consider continuation criteria when/(0, x, p) has noncompact support. In this regime, Luk-Strain [9] proved that f parallel to(LtLxLp1)-L-infinity-L-r less than or similar to 1 is a continuation criteria for theta >5. We improve this result to theta >3. Finally, we build on another result by Luk-Strain [8). The authors proved boundedness of momentum support on a fixed two-dimensional plane is a sufficient continuation criteria. We prove the same result even if the plane varies continuously in time. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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