Local well-posedness
On the local well posedness of a Benjamin Ono Boussinesq system
... linearly well posed if and only if a, c, and d satisfy the relation ...The local well- posedness of the nonlinear system ...locally well posed in the Sobolev space H s ( R ) × H s+1 ( R ...
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Local well-posedness of the generalized Cucker-Smale model with singular kernels
... the local well-posedness of weak solutions to the kinetic C-S equations ...the well-posedness of solutions can not be applied due to the singularity either in position or velocity, and ...
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Local well-posedness for periodic Benjamin equation with small initial data
... the well-posedness for KdV equation is quite rich and the litera- ture ...the local well-posedness of the dispersion generalized periodic KdV equation, see [–] for ...
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On the Boussinesq system: local well-posedness of the strong solution and inviscid limits
... a well studied domain [3–8]. The well-posedness of the Boussinesq system has been studied ex- tensively in recent ...global well-posedness of weak solutions, or strong solutions in the ...
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Local well-posedness and persistence properties for a model containing both Camassa-Holm and Novikov equation
... where the variable u(t, x) represents the fluid velocity at time t and in the spatial direc- tion x, and k is a nonnegative parameter related to the critical shallow water speed []. The Camassa-Holm equation (.) is ...
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Local well-posedness of generalized BBM equations with generalized damping on 1D torus
... Benjamin-Bona-Mahony equation with generalized damping on the one dimensional torus. In contrast to the classical BBM equation, the main difference is that the generalized equation contains two nonlocal operators, and the ...
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The local well-posedness for nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative
... where u(x, t) are complex-valued function, u(x, ¯ t) is the complex conjugate quantity of u(x, t). a, b, and c are real numbers. We are interested in obtaining the well-posedness for the Cauchy problem of ...
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The local well-posedness of solutions for a nonlinear pseudo-parabolic equation
... The local existence and uniqueness of solutions for a nonlinear pseudo-parabolic equation are established in the Sobolev space C([0, T); H s (R n )) ∩ C 1 ([0, T); H s–1 (R n )) with s > n 2 ...
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The local well-posedness and stability to a nonlinear generalized Degasperis-Procesi equation
... In the following, we will give the conservation law in some case for Eq. () in Section . The proof of existence for the local strong solution and its stability to Eq. () are given in Section and Section , ...
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On the well-posedness of the incompressible porous media equation in Triebel-Lizorkin spaces
... the local well-posedness and blow-up criterion for the incom- pressible Euler equations [, ], and quasi-geostrophic equations [] in Triebel-Lizorkin ...is well known, Triebel-Lizorkin ...
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A few remarks on the generalized Novikov equation
... works. Tiglay [] showed the local well-posedness of the problem in Sobolev spaces and the existence and uniqueness of solutions for all time using orbit invariants. For analytic initial data, the ...
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Wave-breaking criterion and global solution for a generalized periodic coupled Camassa-Holm system
... establish local well-posedness for the two-component system and presented some precise blow-up scenarios for strong solutions of the ...the local well-posedness for the ...
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On a model for the Navier–Stokes equations using magnetization variables
... of local well-posedness and global existence for small-data in certain critical spaces, as well as a number of important partial regularity ...global well-posedness for arbitrary ...
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The global stabilization of the Camassa-Holm equation with a distributed feedback control
... Applying Lemmas ., . and using the Littlewood-Paley theory, one may follow sim- ilar arguments to [] to establish the local well-posedness for problem (.) with suit- able modifications. Here ...
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The local strong and weak solutions to a generalized Novikov equation
... locally well-posed in Sobolev space H s with s > by using the abstract Kato ...the local well-posedness for the periodic Cauchy problem of the Novikov equation in Sobolev space H s (R) ...
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Existence of solutions to path dependent kinetic equations and related forward backward systems
... the well-posedness of adap- tive kinetic Equations (5), the local well-posedness and global existence of anticipating and general path depend- ent kinetic equations and finally some ...
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Existence of Solutions to Path Dependent Kinetic Equations and Related Forward Backward Systems
... the well-posedness of adap- tive kinetic Equations (5), the local well-posedness and global existence of anticipating and general path depend- ent kinetic equations and finally some ...
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On the global existence of 3-D magneto-hydrodynamic system in the critical spaces
... the local well-posedness of the three-dimensional inhomogeneous incompressible isentropic Navier-Stokes equations in critical spaces but without the small density ...global ...
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Metric characterizations for well posedness of split hemivariational inequalities
... of well-posedness hemivariational inequalities have been studied since Goeleven and Mentagui [31] firstly introduced the concept of well-posedness to a hemivariational inequality in ...the ...
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Well posed generalized vector equilibrium problems
... is well known, the notion of well-posedness can be divided into two different groups: Hadamard type and Tykhonov type ...of well- posedness for a problem means the continuous dependence ...
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