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This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term $\int_{\mathbb{R}^{n}}\rho\varphi dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data \cite{Kunzinger0001,Wei0001}. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of $\frac{4q-4}{3q-2}$ for $1<q<2$. As a consequence, global existence of weak solutions for general initial data is obtained.
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참고문헌 (14)
참고문헌 신청
C. Bardos / 1985 / Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data / Ann. Inst. H. Poincare Anal. Non Lineaire 2(2):101~118
R. J. Diperna / 1989 / Global weak solutions of Vlasov-Maxwell system / Comm. Pure Appl. Math. 42(6):729~757
R. T. Glassey / 1996 / The Cauchy Problem in Kinetic Theory
R. T. Glassey / 1988 / Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data / Comm. Math. Phys. 119(3):353~384
R. T. Glassey / 1986 / Singularity formation in a collisionless plasma could occur only at high velocities / Arch. Rational Mech. Anal. 92(1):59~90
R. J. Diperna / 1989 / Global weak solutions of Vlasov-Maxwell system / Comm. Pure Appl. Math. 42(6):729~757
R. T. Glassey / 1996 / The Cauchy Problem in Kinetic Theory
R. T. Glassey / 1988 / Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data / Comm. Math. Phys. 119(3):353~384
R. T. Glassey / 1986 / Singularity formation in a collisionless plasma could occur only at high velocities / Arch. Rational Mech. Anal. 92(1):59~90
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