Global Semigroup of Conservative Weak Solutions of the Two-Component Novikov Equation
Constructs a global-in-time semigroup of conservative weak solutions to the two-component Novikov system for initial data in the metric space of H^1 pairs whose derivative product lies in L^2. Passing to Lagrangian/characteristic variables keeps the flow well-posed across wave-breaking, where the energy measures (u_x)^2, (v_x)^2 and (u_x)^2(v_x)^2 may concentrate on a positive-measure set of times; conservation of the H^1 energy singles out the physically relevant solution branch, and the data-to-solution map is shown continuous in the uniform norm.
GLOBAL SEMIGROUP OF CONSERVATIVE WEAK SOLUTIONS OF THE TWO-COMPONENT NOVIKOV EQUATION K. H. KARLSEN
The two-component Novikov system is a pair of coupled integrable evolution PDEs for u(t,x), v(t,x) with momenta m = u - u_xx, n = v - v_xx and cubic nonlinearity; it is a nonlocal (Alice-Bob) system …