Global weak solutions for the relativistic Vlasov-Klein-Gordon system in two dimensions
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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.
Abstract
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.
참고문헌 (14)
- C. Bardos, "Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data", Ann. Inst. H. Poincare Anal. Non Lineaire, 2(2), pp.101~118 (1985)[DOI]
- R. J. Diperna, "Global weak solutions of Vlasov-Maxwell system", Comm. Pure Appl. Math., 42(6), pp.729~757 (1989)[DOI]
- R. T. Glassey, "The Cauchy Problem in Kinetic Theory" (1996)
- R. T. Glassey, "Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data", Comm. Math. Phys., 119(3), pp.353~384 (1988)[DOI]
- R. T. Glassey, "Singularity formation in a collisionless plasma could occur only at high velocities", Arch. Rational Mech. Anal., 92(1), pp.59~90 (1986)[DOI]
- F. Golse, "Regularity of the moments of the solution of a transport equation", J. Funct. Anal., 76(1), pp.110~125 (1988)[DOI]
- S.-Y. Ha, "Global existence of classical solutions to the damped Vlasov-Klein-Gordon equations with small data", J. Math. Phys., 50(5), pp.33~ (2009)
- L. Hormander, "Lectures on Nonlinear Hyperbolic Differential Equations" (1997), Springer Verlag
- M. Kunzinger, "Global weak solutions of the relativistic Vlasov-Klein-Gordon system", Comm. Math. Phys., 238(1-2), pp.367~378 (2003)[DOI]
- M. Kunzinger, "On classical solutions of the relativistic Vlasov-Klein-Gordon system", Electron. J. Differential Equations, 1(1), pp.1~17 (2005)
- E. H. Lieb, "Analysis" (2001)
- K. Pfaffelmoser, "Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data", J. Differential Equations, 95(2), pp.281~303 (1992)[DOI]
- G. Rein, "Global weak solutions to the relativistic Vlasov-Maxwell system revisited", Commun. Math. Sci., 2(2), pp.145~158 (2004)[DOI]
- M. Wei, "Global weak solutions of the relativistic Vlasov-Klein-Gordon system in two dimensions", Ann. Differential Equations, 4(4), pp.511~518 (2007)