Proof: Putting together the lower bound for the lifespan of (θ , u) given by (17) and the uniqueness of smooth solutions, it suﬃces to state that under the assumptions of the lemma, we have 0≤t
Global Existence Results for the Anisotropic Boussinesq System in Dimension Two
So let us assume from now on that s ≥ 3 and let us denote by (θ , u) the maximal solution supplied by Proposition 4, and by T ∗ the lifespan of (θ , u).
Global Existence Results for the Anisotropic Boussinesq System in Dimension Two
Traditional sequential patterns algorithms are founded on the assumption that items in databases are static, and that they existed throughout the whole lifespan of the world modeled by the database.
Temporal Support of Regular Expressions in Sequential Pattern Mining
In many real-world applications, assuming that the values of attributes for a category occurrence do not change (or even that a category occurrence spans over the complete lifespan of the dataset) could not be realistic.
Temporal Support of Regular Expressions in Sequential Pattern Mining
We assume that the category schema is constant across time, i.e., the attributes of a category are the same throughout the lifespan of the category.
Temporal Support of Regular Expressions in Sequential Pattern Mining
Bourgain has proven a mass concentration property for solutions to cubic NLS posed in L2 (R2 ) with a ﬁnite lifespan (T ∗ < ∞).
Mass Concentration for the Davey-Stewartson System
About lifespan of regular solutions of equations related to viscoelastic ﬂuids.
The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids
The lifespan of each individual is an exponential random variable of mean 1.
Recent results on branching random walks
Nevertheless, as in , we are able to compare them to closed ODEs and derive bounds on the lifespan of smooth solutions.
Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation
Taking advantage of the Strichartz estimates and using the special structure of the vorticity we show that the lifespan Tε of the solutions is bounded below by log log log 1 ε , where ε denotes the Mach number.
Low Mach number limit for the isentropic Euler system with axisymmetric initial data
As an application in space dimension two, if we denote by Tε the time lifespan of the solution (vε , cε ) then limε→0 Tε = +∞.
Low Mach number limit for the isentropic Euler system with axisymmetric initial data
To study the lifespan of the solutions we do not use the approach of based on the stability of the incompressible Euler system.
Low Mach number limit for the isentropic Euler system with axisymmetric initial data
Therefore it is legitimate to try to accomplish the same program for the system (1.1) as in the subcritical case and especially to quantify a lower bound for the lifespan of the solutions.
Low Mach number limit for the isentropic Euler system with axisymmetric initial data
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