ترغب بنشر مسار تعليمي؟ اضغط هنا

Local well-posedness and global existence for a multi-component Novikov equation

75   0   0.0 ( 0 )
 نشر من قبل Yuxi Hu
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Considered herein is a multi-component Novikov equation, which admits bi-Hamiltonian structure, infinitely many conserved quantities and peaked solutions. In this paper, we deduce two blow-up criteria for this system and global existence for some two-component case in $H^s$. Finally we verify that the system possesses peakons and periodic peakons.



قيم البحث

اقرأ أيضاً

In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $partial_{t} u+ Delta^2 u=f(u),;t>0,;xinR^N,$ with $f(u)sim mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $f(u)sim u^m$ as $uto 0,$ $m$ integer and $N(m-1)/4geq 2$, we show that the solution is global. Moreover, we obtain a decay estimates for large time for the nonlinear biharmonic heat equation as well as for the nonlinear heat equation. Our results extend to the nonlinear polyharmonic heat equation.
In this paper we consider the problem: $partial_{t} u- Delta u=f(u),; u(0)=u_0in exp L^p(R^N),$ where $p>1$ and $f : RtoR$ having an exponential growth at infinity with $f(0)=0.$ We prove local well-posedness in $exp L^p_0(R^N)$ for $f(u)sim mbox{e}^ {|u|^q},;0<qleq p,; |u|to infty.$ However, if for some $lambda>0,$ $displaystyleliminf_{sto infty}left(f(s),{rm{e}}^{-lambda s^p}right)>0,$ then non-existence occurs in $exp L^p(R^N).$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $|f(u)|sim |u|^{m}$ as $uto 0,$ ${N(m-1)over 2}geq p$, we show that the solution is global. In particular, $p-1>0$ sufficiently small is allowed. Moreover, we obtain decay estimates in Lebesgue spaces for large time which depend on $m$.
207 - Yuzhao Wang 2009
In this paper we consider the hyperbolic-elliptic Ishimori initial-value problem. We prove that such system is locally well-posed for small data in $H^{s}$ level space, for $s> 3/2$. The new ingredient is that we develop the methods of Ionescu and Ke nig cite{IK} and cite{IK2} to approach the problem in a perturbative way.
In this paper we show global well-posedness near vacuum for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and ternary inter actions of particles, and may serve as a more accurate description model for denser gases in non-equilibrium. Well-posedness of the classical Boltzmann equation and, independently, the purely ternary Boltzmann equation follow as special cases. To prove global well-posedness, we use a Kaniel-Shinbrot iteration and related work to approximate the solution of the nonlinear equation by monotone sequences of supersolutions and subsolutions. This analysis required establishing new convolution type estimates to control the contribution of the ternary collisional operator to the model. We show that the ternary operator allows consideration of softer potentials than the one binary operator, consequently our solution to the ternary correction of the Boltzmann equation preserves all the properties of the binary interactions solution. These results are novel for collisional operators of monoatomic gases with either hard or soft potentials that model both binary and ternary interactions.
71 - Elena Kopylova 2019
We prove global well-posedness for 3D Dirac equation with a concentrated nonlinearity.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا